S 1577 
IN7 
topy 1 




Class XS_L2XT 

Book ■\\'^ 

Coppght]^" 



COPXRIGIIT DEPOSIT. 



COTTON 

SPINNERS 

con PAN ION 



PUBLISHED BY I. C. NOBLE 

NEW BEDFORD, 
MASSACHUSETTS, TJ. S. A. 



-^^^,',1 






NEW BEDFORD 
THE A.E.COFFIN PRESS 



'CI.A25J08 



1^1??^ 



A 



The writer has often seen difficulties 
experienced in not having a small vest- 
pocket book handy for reference on 
Textile Machinery Calculations. 

In this book he has tried to fill this 
requirement, and at the same time to 
make the contents as simple and concise 
as possible, so that any person having 
charge of the machines can follow him 
in his explanation when he names the 
pulleys, gears and rolls. I am, 
Yours truly, 

I. C. NOBLE. 



I. C. NOBLE 

ALL KINDS OF 

New TextSe Machinery 
Erected. 



Old Machines Moved 
and Overhauled. 

Mules a specialty. 



1649 Acushnet Ave. 

New Bedford, 

Mass. 



INDEX. 

PAGK 

Cotton 7 . 

Cotton (suitable for yarns) 11 

Cotton Grading 12 

Cotton Sampling 13 

Cotton Mixing 14 

Boilers 15 

Steain Engine . . 17 

Belting 20 

Receipts for Machine Shop 23 

Arithmetic 26 

Table of Square Roots 42 

Hopper Bale Breaker 44 

Automatic Feeder 44 

Opener 45 

Breaker Lapper 46 

Finisher Lapper 47 

Carding 49 

Sliver Lap Machine 51 

Ribbon Lap Machine 51 

Comber 51 53 

Drawing Frame 54 

Fly Frames 57 

Wrapping Plivers, Roving and Yarn. 65 

Setting Rolls 66 

Self-Acting Mule 70 

" (Hetherington's)... 78 

" (Asa Lees) 82 

" (Dobson & Barlow) 92 

Turns of Spindle to one of rim 96 

Ring Spinning Frame 98 

Horse Power required 101 



Howard and Bullough 

AMERICAN MACHINE CO., LD. 
PAWTUCKET, R. I. 



Builders of Bale Breakers, 
Feeders, Openers, Lattices, 
Brealier tappers, Interme- 
diaie and Finisher tappers^ 
Revolving FlatCards, Draw- 
ing Frames, Slubber, Inter 
and Roving Frames, Spin= 
ning Frames, Twisters and 
Cone Winders, 



COTTON. 

Cotton is grown in the United States of 
America, Egypt, China, Corea and South 
America. 

The cotton crop of the United States 
of America is larger than the wliole of 
the other crops combined. 

American varieties are classed in four 
qualities — good ordinary, low middling, 
middling and good middling. 

South American are classed in three^ 
middling fair, fair, and good fair. 

Egyptian, two — fair and good fair. 

East Indian, three — fair, good fair, and 
good. 

The names of the commonly used cot- 
tons are Sea Island, Egyptian, American. 
Brazilian, and Indian. 

There are several other varieties grown, 
but not generally used as the ones 
named. 

The Sea Island cotton is grown on 
islands off the coast of South Carolina 
and Georgia, namely, St. Helena, Port 
Royal, Edisto, John and James Islands, 
St. Simon and Cumberland Islands. It is 
also grown in the State of Florida from 
Sea Island seed. 

This cotton is the most valuable cotton 
grown on account of its length of staple, 
fineness, strength, smoothness, and clean- 
liness, also for the careful ginning it 
receives. 

The fibre is fine, soft, silky, long, and 
regular. 

The American varietv of Sea Island 
cotton is the best. The Fiji and Tahiti 
varieties of this cotton are uncertain in 
their staple. 



Lace and thread are made mostly from 
this cotton. 

The length of staple is from l^i to 2^4 
inches. 

Egyptian cotton is next to Sea Island 
for the making of fine yarns. It is silky, 
strong, and tough. 

The brown Egyptian is generally soft, 
whilst the white Egyptian is hard and 
harsh. 

Gallini is the best of Egyptian cottons 
and is grown from Sea Island seed. The 
staple of Egyptian cottons ranges from 
1% to 11/^ inches. 

American cotton is the staple cotton of 
the world. 

The vast territory covered by the culti- 
vation of this cotton gives us a number 
of varieties and grades; but we can divide 
them into four classes: Orleans, Texas, 
Upland, and Mobile. 

Orleans or Gulf cotton is the best of 
American cottons. It is grown on the 
banks of the Mississippi river and is 
known as Benders, Peelers, and Allan- 
seed. 

Peelers is a good cotton, regular in 
strength and staple, and is very soft and 
pliable. It mixes well with soft Egyptian. 

The length of the Gulf cotton staple is 
from 1 to iy2 inches. 

Mobile and Upland cotton is soft and 
clean, but rather short staple. 

Texas cotton is firmer in staple than 
the INTobile and Upland, but contains more 
leaf, and is not so bright in appearance. 
It is a cotton that will make 32s warp 
or filling. 

The staple is about an inch in length. 

Brazilian cotton has many varieties, as 
well as qualities, some being harsh, 
whilst otliers are soft. 



ir'eruvian mixes well with wool (the 
harsh or rough Peruvian), but the softer 
Peruvian, on account of its color, enables 
it to mix well with Orleans or Gulf 
cotton. 

Its staple Is a little longer than Ameri- 
can generally. It is from 1% to li/^. 

Indian cotton is generally dirty, some of 
it being low in character, and containing 
a large quantity of round and fiat fibres, 
and the fibres are not so uniformly 
twisted as in American cotton. 

The better classes, such as Hingunghat, 
can be mixed with American. 

The length of staple is % of an inch to 
1^4 inches. 

China cotton is a short stapled cotton, 
rather harsh, but very white. It is used 
in China and Russia. 

Cotton is generally planted in April and 
picked in September or October. 

The average yield of lint cotton in India 
is about 75 lbs. per acre. 

American cotton Avlien picked and be- 
fore being ginned contains two -thirds its 
weight of seeds. So, if a man takes newly 
picked cotton to be ginned, and he has 
1000 lbs., he receives 1000x2=2000, 
2000-^3=666 2-3 lbs. of seed, and the re- 
mainder 333 1-3 lbs. cotton fibre. 





biobc 


^■ 


^- 


'-■^' 




C C cc cc yii cd 


!/3 






'^'B ^ u u u 


> 


CCtpl^O o o o 


t, tH Gftft a 


3 O ^ J-' ^5 f^ 


^ 


^ _ CC CC 03 CS 


<s 


&&^^^^ 




03 d . . - . 




> > M w m m 


^ .ooo la 


C:.P.>q^3(M.^ 


'S 


P 13 O O O O 


(« 






OO a i^ft ft 




SSPPPP 


<u 








"& 




55 S' 


:^;S t^ 


C^ M C-3 CQ T-H 


o ^ 


o o c o o;:^ 


c 


+J +J H-J +J -IJ ^_l 




SS¥^2 


M.S 




S 




h^ 












• H-i 




'C 






:w 


U 


^ 








CO 


In ^ 


•.1 1 


;z; 






^•'SSts^s 




w^ 


5fr 


j- 


fe^ 1 



d^ 


>-< —4 


^H 






StSES 


■ 


uu u . 




o o o g 




&&&ft 


ftftftft 


d c6 ce ^ 


Si U U Si 

dddd 


m m" m' . 


« » « « 


O OO w 


W W W M 


i^o coo 


oooo 


„^,--t- 


iaiTJi^ia 


o o o o 


CO O O 


^-^■^-^ 




o,m 01 p. 


ft ftftft 


Pggp 


PPtJp 


;^ 


J^^#^ 


1— 1 


1— 1 rH T-i lH 


o;^;5^#;^ 


o o_o o 






;5^ 








:: 




■ :o : ' 






§ ^ S 


a • " ' 


2 .-ft c6 


gyptia 
allini 
bbasi 
rown 


Brazi 
era . 
ernam 
ariba 
aranh 


H0< 


m^ 


' OO^CM^ 



60 ^^ 




a SI 




>— 1 t— *■ 




F— *■ C 




"S ^^ 


^ &| 


§ da 


I ts 


rT W) tc c 


. in m 


&.Sg? 


> oo 


$sss 


o o 


M 02 a c 


I p-a 




PD 


;^ ;^ 


s ;^. 


T-ll-l T- 


■■-I 


BB^S 


^o 


S^ ^ 


? ^^ 


IH 










c • 








d C 


5 






p>.^ 


i 






^^ > 


J 






.S S-, ;3 


H 


W 


> (iiu 


i} 


-^ M 


SfLn a; 


3 S-^ tr 






c 


t)§ 


h 



02 w to m 


eg eg eg ca 


aaaa 


02 02 02 02 02 


522£2^| 





32 J^: 







COTTON GRADING. 



There are twenty-six different grades, 
namely: 
Fair 

Barely Fair 

Strict Middling Fair 

Fully Middling Fair 

Middling Fair 

Barely Middling Fair 

Strict Good Middling 

Fully Good Middling 

Good Middling 

Barely Good Middling 

Strict Middling 

Fully Middling 

Middling 

Barely Middling 

Strict Low Middling 

Fully Low Middling 

Low Middling 

Barely Low Middling 

Strict Good Ordinary 

Fully Good Ordinarj^ 

Good Ordinary 

Barely Good Ordinary 

Strict Ordinary 

Ordinary 

Low Ordinary 

Inferior 

The Full Grades are Fair, Middling 
Fair, Good Middling, Middling, Good 
Ordinary, Ordinary. 

The Half Grades are termed "Strict." 

The Quarter Grades are termed "Bare- 
ly," coming between the half grade and 
the above full grade. The term "Fully" 
means between the half grade and the 
next full grade below it. 

The qualities to observe in sampling 
or grading cotton are: Length of Staple. 
12 



Regularity of length and diameter of 
staple. Fineness. Strength, Smoothness, 
Color, and Cleanliness; also see that the 
fibre has not been cut when ginning. 

The cotton becomes full of sand during 
wind storms; see that it is as free from 
sand as possible. 

COTTON SAMPLING. 

Take 100 lbs. of cotton, shake it well 
and the sand will drop out; weigh the 
sand and you -then get the percentage of 
loss through this source. 

During heavy rains it becomes stained 
with the earth. See that it is not stained, 
especially if you are going to spin filling; 
but if you are going to size the yarn, you 
do not require to be so particular, as 
there can be bought a cotton a little 
cheaper, of good staple, but stained a 
little, which can be covered by sizing. 

See that there is not too much leaf in 
the cotton, and that it is not dirty. 

Look out for dampness; it always con- 
tains a certain amount, absorbed from 
the atmosphere (about 89c). 

On one thing always be very particular. 
Always deal with reliable cotton brokers. 

Look at the brightness of your cotton 
or "bloom," as it is called. 

Bagging and Ties m.ust not exceed 22 
lbs. per bale. 

The average allowance for loss of 
weight on any one mark of cotton shall 
not exceed three pounds per bale, with 
cotton in sound and dry condition. 

Cotton is valued according to its char- 
acteristics that best adapt it to the use 
for which it is intended. 

13 



COTTON MIXING. 

In mixing cottons be careful that you 
get equal length of staples. 

Do not mix a harsh and silky cotton 
together, except for special purposes. If 
you wish to imitate wool get rough Peru- 
vian. 

Always mix as large mixing as possible, 
as it keeps the drafts on your machines 
equal and saves time in the setting and 
resetting of rolls. 

Pay attention to the mixings, and 
picker room generally, as there lies a 
part of your foundation for an even yarn. 

The shorter stapled Sea Island mix 
well with Best Egyptian for 80s to 120s 
yarns. 

Peeler and Soft Egyptian also mix well 
to spin from 60s to 80s yarn. 

Gulf, Texas, and Soft Peruvian mix well 
for yarns of 40s to 60s. 

Rough Egyptian and Rough Peruvian 
incorporate well, and are suitable for 
spinning yarns from 40s to 50s. 

The better class of Indian cotton 
(Hingunghat) is mixed with the lower 
classes of American cotton — Georgia or 
Boweds. Mix also with Oomrawuttee, 
Broach, and others. 

If a mixing of bales — say, 24 bales has 
to be mixed — divide them as much as 
possible at the feeder. 

Say we have 8.X.Y.Z., 8.G.H.I. and 
8.A.B.C. Spread one X.Y.Z. on a large 
floor space. On the top of this throw 
one G.H.I. Over the top of these spread 
one A.B.C. and keep repeating this until 
the 24 bales are finished. 

The mixings given here are only a few 
of the many different mixings made in 
our mills. 

14 



BOILERS. 

Rule for Calculating Strength of Cylinders 
and Boilers. 

The tenacity of the metal of which a 
boiler is constructed is about 60,000 lbs., 
or six- sevenths of that of good wrought 
iron, a bar one inch square being the 
standard. 

As the cylinder which constitutes the 
boiler is not whole, or in one piece welded 
together, but -is composed of a number of 
plates riveted together, the plates being 
cut away for the holes, it is necessary 
to diminish the number, which expresses 
the strength; therefore let the tenacity 
be put at 30,000 lbs. 

This boiler is 7 feet 6 inches diameter. 
Thickness of plates % of an inch. 

Multiply the numerator of the thickness 
by the tenacity of the metal, and multi- 
ply the denominator by half the diameter 
of the cylinder in inches, then divide the 
numerator by the denominator and the 
answer will be the strength, or bursting 
pressure. 

Example. The denominator of %: 
Dia. 7 ft. 6 in. 4-2=45 ins. 

45 X 8=360 
30000 tenacity of metal. 

3 numerator of % plate. 



360)90000(250 bursting pressure. 

720 

1800 
1800 

Then we get 250 lbs. bursting pressure. 
This is if the iron is good and all things 
in proportion. 

15 



INCRUSTATION OF BOILERS. 

1. Potatoes, one-fiftieth of weight of 
water prevents adherence of scale. 

2. Twelve parts salt, 2% caustic soda, 
% extract of oak bark, % of potash. 

3. Pieces of oak-wood suspended in 
boilers, and renewed monthly prevents 
deposit. 

4. Two ounces of mtiriate of ammonia 
in a boiler twice a week prevents incrus-- 
tation and decomposes scale. ^ 

5. Molasses fed into a boiler prevents ' 
incrustation. 

6. Carbonate of soda. 

7. Chloride of tin. 

8. Spent tanners bark. 

9. Frequent blowing off. 

10. Mahogany or oak sawdust in lim- 
ited quantities. 

The tannic acid attacks the iron, so 
this should be used with caution. 



BOILERS. 

Fuel — Average Evaporative Power. 

One pound of coke evaporates 9 lbs. off 
water. 

One pound of coal evaporates 9 lbs. off 
water. 

One pound of oak (dry) evaporates iVz •. 
lbs. of water. 

One pound of slack evaporates 4 lbs. of' 
water. 

(Feed water supplied at 212° for above.) 

Coal loses about one-third in coking (of 
its weight), but increases in bulk one- 
tenth. 1 



STEAM ENGINES. 

■ Horse power in engines is calculated 
as the power which would raise 33,000 
lbs. a foot high in a minute, or 90 lbs. at 
the rate of four miles an hour. 

Always keep the cylinder hot and dry. 
Look to the mode of fitting the steam- 
pipes. 

A nominal horse power of an engine, as 
was mentioned before, is to move 33,000 
lbs. one foot high per minute, or say 150 
lbs. raised 220 feet per minute, which 
means the same thing, for if we multiply 
150 by 220 it equals 33,000. 

For one horse power, multiply 220 by 
22 circular inches. This gives 4840. Then 
multiply by the pressure 7 lbs. We get 
33,880, and divide by 33,000 lbs., and the 
result is one horse power. 

Example: 

220 



440 
440 



4840 



33000)33880(1 horse power. 
33000 



880 
. Desaguliers figures that a horse walks 
2% miles an hour against a resistance of 
200 lbs; this is at the rate of 220 feet per 
minute. A horse power is therefore eoual 
to a force that will raise 44,000 lbs. one 
'oot per minute when working eight hours 
3er day. 
Mr. Watts found that a horse treading 
17 



a mill path at the rate of 2% miles an 
hour raised 150 lbs. by a cord hanging 
over a pulley, which is equivalent to 
raising 33,000 lbs. one foot high a minute. 
His steam engines were calculated to 
work at 44,000 lbs. per horse power, but 
he allowed 33,000 lbs. in his calculations, 
considering the difference due to friction. 



How Horse Power is Calculated. 

1760 yards one mile, a horse walking 
2% miles per hour against a force of 150 
lbs. working 8 hours per day. 

Work this out, and we find it is equal 
to raising 33,000 lbs. one foot per minute. 



Example; 



1760 yds. in a mile. 
2.5 miles per hr. 

8S00 
3520 



44000 
3 


ft. in a yard 


132000 
150 


Hd. resistanc* 


6600000 
132000 



Mins. in hour=:60)1980000.0(33000=l h. p. 
180 

180 

180 



18 



1 

I 



Horse Power of an Engine. 

Muiciply area of piston in square inches 
by mean effective pressure of the steam 
on the piston per square inch, and mul- 
tiply these by velocity of piston per min- 
ute, and divide by 33,000. 



Example: 


45 dia. of piston. 
45 




225 
180 




2025 sq. in. in piston. 
360 speed of piston. 




121500 
6075 




729000 

20 avg. pres. piston. 


ivide by 33000)14580000(441 h. power. 
132000 




138000 
132000 




60000 
33000 



How to Find a Pipe to Supply a 36-Inch 
Cylinder. 

Multiply the diameter of cylinder by 
.96; this will give area, from which you 
find diameter. 

19 



Example: 

36 



216 

324 



Decimal area .7854)345600(44 sq. inches. 
31416 

31440 
31416 



Find square-root of 44. 
6)44(6.63 Answer. 
36 

126)800(6 
756 

1323)4400(3 
3969 

6.63 inch pipe required. 



BELTING. 
To Find Speed of Belt Per Minute. 

Rule: — Multiply circumference of thi 
pulley on which belt is running by th« 
revolutions of the shaft. 

Suppose your pulley is 24 inches or 
feet, and revolutions of shafting are 20( 
per minute. Proceed as follows: 

2X3.1416X200=1356 feet per minute. 



20 



To Find Horse Power a Single Beit Will 
Carry from One Pulley to Another. 

Rule:— Multiply the width of the belt 
reduced to inches by 45 and by the feet 
the belt travels per minute, and divide 
the quotient by 33,000. 

Suppose a single belt travels 1356 feet 
per minute and the belt is 1 foot and 4 
inches wide (equal to 16 inches). 

Example: 

16X45X1356=976320 



33000 = 33000 
976320 divided by 33000=29.58 horse power 

To Find the Horse Power of a Double 
Belt. 

Rule: — Proceed exactly as you did in 
finding single belt, only multiply by 75 
instead of 45. 

Example: 

16X75X1356=1627200 



33000 = 33000 
1627200-^33000=49.3. 



To Find a Single Belt Required to Give a 
Certain Horse Power. 

Suppose you require 30 horse power and 
the belt will run 2000 feet per minute. 

Rule: — Multiply the 30 horse power re- 
quired by 33,000. Take this for the divi- 
dend. Then multiply the number of feet 
the belt travels per minute, 2000 by 45. 
Example: 30X33000=990000 



2000X45 = 90000 
990000 divided by 90000=11 inch single 
belt required. 

21 



To Find Double Belt Required to Give a 
Certain Horse Power. 

Rule: — Proceed exactly as when finding 
single belt, but use 75 instead of 45. 

Example: 

30X33000=990000 



2000X75=150000 



990000^150000=6.6 inch double belt re- 
quired. 

In testing the horse power required to 
run the shafting alone, and then to run 
the whole load of the mill, I would say 
that a fair percentage is 25 per cent., or 
say a mill requires a hundred horse power 
to run the shafting and belts alone, it 
should not require more than 400 horse 
power to drive the whole mill load. If 
it does, look to your belts; a tight belt 
makes hot bearings, requires more power 
to drive, and runs the machine no 
quicker. A large quantity of coal can be 
saved by having the belts at a right 
tension. 

Tight belts ruin the bearings, cost more 
to run, and do not increase production. 



I 



RECIPES FOR MACHINE SHOP. 

1. Mixture for welding steel is: One 
salammoniac and ten parts borax. Pound 
these together and fuse until clear; pour 
out, and when cool reduce to a powder. 

2. Tempering Turning Tools. 

When the rature of the steel is un- 
known, it is a good plan to heat the tool 
and try with a file at the different shades 
of color, and when the file is felt to bite 
the least bit, quench the tool. 

This should be done by daylight, as 
pale straw color is difficult to see in 
artificial light. 

3. Tempering Steel Springs. 

Wet the spring (hardened) with olive 
oil, turn it gently round on the fire till 
it catches a light. If it is a very par- 
ticular job, take a pan and boil in oil. 

4. Hardening Tools. 

Heat the tool to a blood-red heat and 
plunge it into common oil, and it will be 
all right for turning purposes. 

5. Solder for Brass. 

One-half lead and half tin, with a little 
resin. This solder will adhere to iron, 
but first rub the iron on a piece of tin. 

6. Solder for Lead. 

Melt one part of block tin, and when 
fusing add two parts of lead. Use resin 
with this solder. 

-23 



7. For Brazing Iron. 

Good brass and a little borax. 

8. Uniting IVIetals. 
For uniting wrought and cast iron, or 
Fteel. Take 20 parts (by weight) of, 
wrought iron fillings. 10 of salammoniac, 
rr.d 5 of balsam of copaiba, melt together 
and beat until dry and hard. This will 
join metals and fill in holes, cracks, or 
other defects, in iron or steel plates. 

9. Welding Cast Steel. 

One ounce powdered glass, one ounce 
salammoniac, and 16 narts borax. For 
mild steel, borax may be used alone 

10. Cement. 

A strong glue is made by adding pow- 
dered chalk to common glue when melted 
and a srlue to resist warmth may be made 
by boiling one pound of common glue in 
two quarts of skimmed milk. 

11. A Good Wheel-Grease, 

Twenty- five lbs. of tallow, 25 lbs. of tar, 
15 lbs. of soda, and ZVz gallons of water 
Boil water and soda, th'^n add tallow and 

12. Black Varnish. 
One pint of vitriol and two gallons o: 
gas tar. Apply after effervescence has 
nearly finished. 



13. Lubricating Mixture. 

Sixteen ounces of good lard, 2 ounce; 
of bee's wax, 8 ounces of flour of sulphur, 
4 ounces of black lead, 16 ounces of white 
soap. 

24 



I 



14. To Keep Shafting Cool. 

Mix white lead and oil to the consist- 
ency of cream. 

15. Dubbing. 

Two lbs. of black resin, 1 lb. of tallow, 
and 1 gallon of train oil. 

16. Lacquering Brass. 
Boil the brass in a solution of potash 
and soda, after which dip them in aqua- 
fortis, 3 parts water. Wash them in 2 
waters and rub in sawdust. Place on a 
gas stove; when warm brush them, then 
apply laccfuer. Put the work on the stove 
with brown paper over it. 

17. Case Hardening. 

Place horn, hoof, bone dust, or shreds 
of leather, together with the article to 
be case hardened, in an iron box, heat to 
blood red, then dip article in cold water. 

Some engineers add white wine vine- 
gar and salt. 

18. Case Hardening With Prussiate of 
Potash. 

Polish the article, then heat to a bright 
red; rub the surface over with prussiate 
of potash, and when a dull red, dip in 
water. 

19. Case Hardening iVIixtures. 

Two of prussiate of potash to one of 
salammoniac mixed. 

Or 2 of salammoniac. 2 of bone dust and 
1 of prussiate of potash. 

20. Cold Soldering Without Fire. 

Bismuth 14 ounce, quicksilver 14 ounce, 
25 



block tin filings 1 ounce. Spirits of salt 
1 ounce. Mixed together. 

21. Cold Brazing Without Fire or Lamp. 

Floric acid % ounce, oxymuriatic acid 
% ounce, mix in lead bottle, put a chalk 
mark at each side you want to braze. 

This mixture will keep about six 
months in a lead bottle. 



ARITHMETIC. 

Before dealing with the drafts and 
twists in the machines, a few examples 
in arithmetic will help us. 

The signs used in calculation are: — ■ 

+ meaning, add. 

= means equal to. 

— signifies subtraction. 

X means multiplied by. 

-=- meaning divided by. 

V signifies that the square root of the 
numter to which it is prefixed is required, 

V signifies that the cube root is re- 
quired. 

' means feet. 

" meaning inches. 

Examples: 

If we write 20 + 4=24, vre mean 20 add 
4 equals 24. 

Then 20 — 4=:=16 is 20 subtract 4 equal 
16. 

20x4=80. This meaning 20 multipliec 
by 4 equals 80. 

2')-=-4=:5 signifies 20 divided by 
equals 5. 

>/16=4 meaning square of 16 equals 4. 

^'27=3 signifies that cube root is re- 
quired 27 equals 3. 

26 



ad 

I 



Multiply 3 by 3 equals 9, which is 
square. Multiply 9 again by 3 and you 
have cube 9X3=27. 

7'-6" means 7 feet 6 inches. 



CANCELLATION. 

If this is used when taking pulleys or 
gears as driver or driven and cancelled 
it makes what would be a very long sum 
short. 

If an 18 inch pulley was driving a 9 
inch pulley, and on the same shaft with 
the 9 inch pulley was a 10 inch pulley, 
driving a 5 inch pulley, now w^e should 
place them thus: 

18X10 meaning 18 multiplied by 10. 



9X5 and 9 multiplied by 5. 
(Note the drivers are on the top or 
above the line, and the driven under.) 
Then we get 

18X10=180 180^45=4 



9X 5= 45 
by multiplying 18 and 10 we get 180, and 
the 9 by 5 we get 45. Then divide the 
180 by 45 and we find 4 revolutions. Thus 
meaning that if we turned the IS inch 
pulley round once, the 5 inch pulley would 
revolve 4 times, if there was no slippage. 
But this is not calculation. 



27 



What I was leading up to was this: 
If we were to cancel these figures it 
would make a very short sum, thus 

2 2 

1^ X ,10 

= 4 Ans. 

p X .5 
As you cancel one number in anothe 
draw a line through them. The 9 goes 
twice into 18, and the 5 goes twice info 
10, so that you have only a 2 over the 
18, and a 2 over the 10, and when mul- 
tiplying these you have: — 

Twice 2 are 4, which is the answer 
Never cancel one number in the bottom 
line figures with another number in th( 
bottom line. Always find a number h 
the bottom line that will cancel with on( 
in the top line, and vice-versa. 

Example: 7 3 6 1 

/7p X U X ^4 x p^ 



I 



10 X 1^ X 14 X P 
Now 10 will go into 70 seven times. 
15 will go into 45 three times. 
14 will go into 84 six times. 
8 will go into 96 twelve times. 
Multiply the 7, the 3, the 6, and the 1 
and the answer is 7X3X6Xl2=il512 Ans. 
Another example: 



1 


] 


? 


2 


^0 


X 1^ 


^ 


X U 


^ 


'^ 


1 


1 



/7 = 1 

— = 1 An 



i 



X^ 



The 18 goes into the 36 twice. The 7 
into 14 twice. The 6 into 12 twice. Then 
the two twos above the line and the two 
twos below the line cancel, thus leaving 
1 for a divisor and 1 for a dividend. 

Ore in one is one, so one is the answer. 

If you did not use cancellation here, 
you would have to multiply the 36, 12 
and 7 together, and then multiply the 6, 
14 and 18 together, and divide one by the 
other. 

Never cancel a decimal and whole 
number. 



PROPORTION. 

Is the equality of two ratios. 
: :: : signifies proportion, as 2 : 4 :: 8 : 16. 

This meaning, as twice two are four, 
twice eight are sixteen. It can be writ- 
ten 2 is to 4 as 8 is to 16. 

When you see that your answer must 
be larger, multiply the two larger num- 
bers together and divide by the smallest 
number, but if the answer is to be 
smaller, multiply the largest and smallest 
number together and divide by the inter- 
mediate number. 

For example: 

20 cards produce 3000 lbs. per day, what 
weight will 50 produce? We know 50 
cards will produce more than 30 similar 
cards, so our answer will be greater. 
Then multiply the two larger numbers 
together and divide by the smallest. 

50x3000=15000 and 
15000^ 20= 7500 lbs. Answer. 



PERCENTAGE. 

This is very useful in mill business. 

The term per means by, or on the, 
and centum means a hundred. So Per- 
centage means on the hundred. 

Thus 6 per cent, means 6 of every 
hundred. Instead of writing per cent., 
the symbol is used %, or it may be placed 
by a fraction, as 6/100, or as a decimal, 
thus, .06. 

Example: 

A man has 60 ring frames, but they are 
only 20 per cent, of what he will have 
when the mill is fully furnished. How 
many will he have? 
Per cent. 20)60 percentage running. 



100 
300 



Divide the percentage of the frames 
Tunning by the rate per cent., multiply 
by a hundred. 

60 is the percentage of frames running 
and 20 per cent, of the whole number. 

When we say he has 20% of the whole 
running, we mean 20 of every 100, so he 
has 300, or 3 times 20=60, which proves 
the 303 to be correct. 

Instead of multiplying by the 100, add 
two ciphers. 

60 H- 20=3 add 2 ciphers 300 

When the principle and the rate per 
cent, are given, it is simple to find the 
interest. 

30 



A man borrows $500 at 7 per cent, per 
annum. What must he pay yearly? 
500X7=3500 and 3500^100=35 dollars 
yearly. 

The better plan is to cross off the two 
last ciphers instead of dividing by the 
100. Thus:— 500X7=35. 

A bale of cotton weighs 500 lbs., and 
after it has gone through the card- room 
processes, the roving made from it 
weighs 400 lbs. What percentage went 
to waste? 

500 — 400=100 lbs. waste 

100X100=10,000 and 10,000-f-500=20%. 

So we see that 20 per cent, went to 
waste. 



FRACTIONS. 

A Common Fraction is one in which 
the unit is divided into any number of 
equal parts. 

The Denominator is the number of 
equal parts into which the unit is divided. 

The Numerator tells us how many 
equal parts are taken. 

When we write 2/3, ask how many 
thirds? Why two, so it tells us how 
many of the figure under the line are 
taken. 

Take % for instance: — the 4 shows how 
many parts the unit is divided into, and 
we are taking 3, when we say %. 

An improper fraction is when the 
numerator, or the figures above the line 
are greater than the denominator or the 
figures below the line, 7/5, 9/4, 6/5. These 
are all improper fractions. 
31 



To reduce urits or mixed numbers to 
improper fractions. 

How manj^ thirds are there in 7 2/3? 

Multiply the 7 by the 3 and add the 
2.7x3=21+2=23/3. To prove this divide 
the 23 by 3 and we get 7 with 2 over, 
which are thirds. 

To reduce improper fractions to mixed 
numbers. 

How many units are there in 28/4? 
Divide the 28 by 4, which equals 7 



Addition of Fractions. 

How many eights are there in i^ 
and %? 

% is equal to 4/8, and % is equal to 6/8. 

4/8 and 6/8 added equals 10/8, which is 
an improper fraction, 10/8-^8/8=1 2/8, and 
the 2/8 when cancelled equals a 1/4, so 
our answer is 1 1/4. 

Add 4/7 and 3/4 and 11/14. 
Rule: — Reduce the fractions to a com- 
mon denominator, add the numerators, 
and let the denominator or figures under 
the line remain as they are. 
Example: 4 3 11 

— +— +— 
7 4 14 

You take the 4/7 and multiply both 
these figures by the denominators, or 
figures under the line, of the other two 
fracti-ins, this meaning by the 4 and 
the 14. 

32 



Do the same with tlie %, multiply the 

3 and the 4 by the other two denomina- 
tors, the 7 and the 14. Now take the 
11/14 and multiply these by 7 and 4, the 
denominators of 4/7 and 3/4. 

Take the denominators of the 4/7 and, 
3/4 and 11/14. Multiply these, the 7, the 

4 and the 14, which equals 392, and this 
is the least common denominator. 



4X 


4Xl4=r224 


7X 


4xl4=r392 


3X 


7X14=294 


4X 


7X14=392 


11 X 


7X 4—308 



14X 7X 4=392 

Now thej' all have a common denomi- 
nator, or, in other words, the three 
figures under the line are the same, and 
it now becomes a simple addition sum, 
by adding the numerators, which are 224 

nd 294 and the 308, but we keep the de- 
nominator just the same. 

224+294+308=826 or 826/392. 
826/392 is an improper fraction, so we 
must divide 826 by 392. 

392)826(2 42/392 
784 

42 

The answer being 2 42/392, but the 
42/392 can be cancelled by dividing the 
enumerator and denominator bv 14: we 
:et 3/28, making the answer 2 3/28. 



Subtraction of Fractions. 

Subtract 15/28 from 31/35. 

Now to do this we must have the frac- 
tions similar, so they must be reduced 
to a common denominator, or, in other 
words, the figures under the lines must 
be the same. 

To do this multiply the first fraction 
15/28 by the denominator of the other 
fraction. 

15X35=525 



28X35=980 



Follow this by multiplying the two 
numbers of the other fraction. Those are 
the 31 and 35 by the denominator of the 
first fraction; this is 28. 

7 
31 X 28 = 858 525 U^ = 7 

35 X 28 = 980 980 ^^^ 20 

20 

Now both denominators are similar, 
and it becomes a simple subtraction sum. 

Subtract 525 from 868=343. 

Let the denominator remain as it was, 
then we have 343/980, and finding 49 will 
divide into the numerator and denomina- 
tor, thus bringing our answer 



H% 



20 



34 



Multiplication of Fractions. 

Multiply 11/12 by 9. 

Multiply the 11 by 9, which equals 99. 
Let the denominator remain as it was 
and we get 99/12, which is an improper 
fraction, so divide the 99 by 12, which 
gives us 8 3/12, or, when cancelled, for 
the 3 will divide into 12 four times, we 
get the answer 8 14. 



Multiply 35/54 by 36/49. 



5 


2 




r^ 


X n 


10 


— 


— = 


= — Answer. 


H 


X ^^ 


21 


3 


7 





By cancelling the 35 and 49, or, in other 
words, dividing each by 7, we get 5 and 7 
instead of 35 and 49, and by dividing 36 
and 54 by 18 we get 2 and 3. Multiply 
the 5 by the 2, we have 10 above the 
line; then multiply the 7 and 3, which 
equals 21, and our answer is 10/21. 



Division of Fractions. 



Divide 96/115 by 6. 

Divide the numeral 
anominator remains 
96^6=16. 16/115. Answer. 



Divide the numerator 96 by 6 and the 
denominator remains the same. 



Divide 32/49 by 4/7. 

Multiply the dividend by the divisoi 
inverted. 

Or, in other v^^ords, place the 7 where 
the 4 is, and 4 where the 7 is, and mul- 
tiply. 



• 3^ X / 8 1 

— — = — = 1 — Answer, 

^^ X ^ 7 7 

7 

4 goes into 32 eight times. 

7 goes into 49 seven times. 

"We get 8/7, which is an improper frac- 
tion; divide the 8 by the 7 and we get 
1 1/7 for our answer. 



FRACTIONS (Complex). 

These are fractions that have theii 
numerators or denominators, or both, 
fractional. 



Example : 
15 



— 4 

19 ;^ X J^ 4 1 

45 ;^ X ^^ 3 3 



3 



76 



Rule: — Invert the denominator and di- 
vide by the numerator. 

This is similar to dividing one fractioi 
by another. 



DECIMALS. 

A Decimal Fraction is a number of 
tenths, hundredths, thousandths, etc. 

A Decimal Fraction is shown by plac- 
ing a dot, or a point, before the numera- 
tor, and not expressing the denominator. 

If we were to write 1.5 in decimal frac- 
tions, we would express it in fractions 
as 1 5/10, or, when the 5/10 are cancelled, 
it is iy2. That is expressing a decimal 
fraction in tenths. When it is written 
1.05 it means hundredths, as 1 5/100, and 
so on, as in thousandths 1.005=1 5/1000. 

The symbol of a decimal is termed 



decimal point. 

.25 = 



1 
4 



To Reduce a Common Fraction to a 
Decimal. 

Reduce % to a decimal. 
Add ciphers to the numerator 3 and 
divide by the denominator. 

3,00-^4=.75 Answer. 

It is exactly like saying $1 — 75 cents, 
meaning one whole dollar and 75 hun- 
dredths of another dollar, or %. 

In adding decimals write the numbers 
so that the decimal points come under 
each other: as, 24.33 + 146.33 + 63.175. 



White thus: 

24.33 
146.33 
63.175 



233.835 Answer. 
This written as a fraction, 233 835/1000 

Subtraction of decimals is similar tc 
addition in keeping the points under eaci 
other. 

Subtract 123.25 from 212.758. 

212.758 
123.250 



89.508 



Multiplication of Decimals. ■ 

Suppose we multiply with the last two 

figures decimals, and the last two figures 

in the multiplicand decimals, then there 

are 4 decimals in the answer or product. 

Example: 

4.25 
2.25 



21.25 
85.0 
.50 



9.5625 Answer, 
or a little over 9^^. 



Division of Decimals. 

Is exactly similar to simple division, 
only the place for the points. 
Example: Divide 20.7888 hy 4.26. 
4.26)20.7888(4.88 Answer. 
17.04 



3.748 
3.408 



3408 
3408 



Rule: — Deduct the two decimals in the 
divisor from the four decimals in the 
dividend. This leaves two, so we have 
two in our answer. 

SQUARE ROOT. 

In finding the square root of 92, mul- 
tiply a number by itself and the one 
that will come under f 2, but nearest to it. 
You could not say 10 times 10 because 
that w^ould be higher than 92, but you 
could say 9 times 9^ so you know the 
square root of 92 is between 9 and 10, or 
9 and a fraction. 

Example: Extract square root of 92. 
9)92(9.591 Answer 
81 




19181)31900(1 
19181 



In taking 92 for the number, you say 
9 times 9 are 81. Commence by dividing 
92 by 9, which gives 9 and 11 remaining; 
to the 11 add two ciphers, which wil 
make the 11 into 1100. Then multiply th< 
9 which is in the answer by 2, whict 
will make it 18. This you put to divide 
in the 1100, but you must put anothei 
figure after the 18, and this figure must 
be the number of times 18 and the figure 
placed after it will divide into 1100. 

A good plan is to put a cipher afte; 
the 18, which makes it 180, divided int< 
1100 would go 5 times. Then you plaG< 
the 5 after the 18 instead of the cioher 
making it 185 divided into 1100, which is 
5 times with 175 remaining. You agair 
place two ciphers after the 175, making 
it 17500. 

The answer as far as you have gone is 
9.5: multiply this by 2 and get your next 
divisor, 95 multiplied by 2 equals 190 
But you must place another figure aftel 
this before dividing the 17500 by it. D( 
as 3'ou did before, place a cipher aftel 
the 190, making it 1900; now see ho^^ 
many times it will divide into 17500, anc 
you find 1900 will divide 9 times with 
remainder of 319. You repeat what 5^01 
did to get the 5 and the 9. That is, yoi 
add two ciphers to the 319, making i 
31900. 

Multiply the answer again by 2. Tha 
is 9.59X2=1918; add a cipher, makinj 
19180; now see how many this will divide 
into 31900. You find it divides 1 time, S( 
take awav the cipher from 19180 an( 
make it 19181; divide this into 31900 am 
you get 1. 



40 



This is quite far enough to take it; in 
fact, for ordinary purposes, 2 decimals 
are far enough to go, but you see by our 
answer we have gone as far as 3 deci- 
mals, the answer being 9.591, which is 
the square root of 92. 

What is the square root of 10? 

3)10(3.16 
9 




NUMBER WITH SQUARE ROOTS GIVEN. 



NO. S 


square 


No. 


Square 


No. 


Square 


Root 


Root 


Root 


.0625 


.25 


12 


3.464 


47 


6.855 


.125 


.353 


13 


3.605 


48 


6.928 


.25 


.5 


14 


3.741 


49 


7.0 


.375 


.61 


15 


3.872 


50 


7.071 


.5 


.71 


16 


4.0 


51 


7.141 


.625 


.79 


17 


4.123 


52 


7.211 


.75 


.866 


18 


4.242 


53 


7.28 


.875 


.935 


19 


4.358 


54 


7.348 


1. 


1.0 


20 


4.472 


55 


7.416 


1.125 


1.061 


21 


4.582 


56 


7.483 


1.25 


1.119 


22 


4.69 


57 


7.549 


1 375 


1.172 


23 


4.795 


58 


7.615 


1.5 


1.23 


21 


4.898 


59 


7.681 


1.625 


1.273 


25 


5.0 


60 


7.745 


1.75 


1.38 


26 


5.099 


61 


7.81 


1.875 


1.37 


27 


5.196 


62 


7.874 


2 


1.414 


28 


5.291 


63 


7.937 


2.25 


1.5 


29 


5.38i 


64 


8. 


2.5 


1.58 


30 


5.477 


65 


8.062 


2.75 


1.65 


31 


5.567 


66 


8.124 


3 


1.732 


32 


5.656 


67 


8.185 


3.25 


1.8 


33 


5.744 


68 


8.246 


3.5 


1.87 


34 


5.830 


69 


8.309 


3.75 


1.93 


35 


5.916 


70 


8.366 


4 


2.0 


36 


6.0 


71 


8.426 


4.25 


2.06 


37 


6.0S2 


72 


8.485 


4.5 


2.12 


38 


6.164 


73 


8.544 


4.75 


2.18 


39 


6.245 


74 


8.602 


5 


2.236 


40 


6.324 


75 


8.66 


6 


2.449 


41 


6.403 


76 


8.717 


7 


2.645 


42 


6.48 


77 


8.774 


8 


2.828 


43 


6 557 


78 


8.831 


9 


3.0 


44 


6.633 


7^ 


8.888 


10 


3.162 


45 


6.708 


80 


8.944 


11 


3.316 


46 


6.782 


81 


9 



42 



No. 


Square 


No. 


Square 


No. 


Square 


Root 


Rool 




Root 


82 


9.055 


122 


11.045 


162 


12.727 


83 


9.11 


123 


11.09 


163 


12.767 


84 


9.165 


124 


11 135 


164 


12.806 


85 


9.219 


125 


11.18 


165 


12.845 


86 


9.273 


126 


11.224 


166 


12.884 


87 


9.327 


127 


11.269 


167 


12.922 


88 


9.38 


128 


11.313 


168 


12.961 


89 


9.433 


129 


11.357 


169 


13 


90 


'.).486 


130 


11.401 


170 


13.038 


91 


9.539 


131 


11.445 


171 


13.076 


92 


9.591 


132 


11 489 


172 


13.114 


93 


9.643 


138 


11.532 


173 


13.152 


94 


9.695 


134 


11.575 


174 


18.19 


95 


9.746 


135 


11.618 


175 


13.228 


96 


9.797 


136 


1 1 . 661 


176 


13.266 


97 


9.846 


137 


11.704 


177 


13.304 


98 


9.89:0 


138 


11.747 


178 


13.341 


99 


9.949 


139 


11.789 


179 


13.379 


100 


10.0 


140 


11.832 


180 


13.416 


101 


10.049 


141 


11.874 


181 


13.453 


102 


10.099 


142 


11.916 


182 


13.49 


103 


10.148 


143 


11.958 


lt:3 


13.527 


104 


lO.lyS 


144 


12 


184 


13.564 


105 


10.246 


145 


12.041 


185 


13.601 


106 


10.295 


146 


12.083 


186 


13.638 


107 


10.344 


147 


12.124 


187 


13.674 


108 


10 392 


148 


12.165 


188 


13.711 


109 


10.44 


149 


12.206 


189 


13.747 


110 


10.488 


150 


12.247 


190 


13.784 


111 


10 535 


151 


12.2^8 


191 


13.82 


112 


10.583 


152 


12.328 


192 


13.856 


113 


10.63 


153 


12.369 


193 


13.892 


114 


10.677 


154 


12.4(i9 


194 


13.JJ28 


115 


10.723 


155 


12.449 


195 


13.964 


116 


10.77 


156 


12.49 


196 


14 


117 


10.816 


157 


12.529 


197 


14.035 


118 


10.862 


158 


12.509 


198 


14.071 


119 


10.908 


159 


12.609 


199 


14.106 


120 


10.954 


160 


12.649 


200 


14.142 


121 


11 


161 


12.688 







43 



Troy Weight. 

24 Grains:=l Pennyweight. 
20 Pennyweighls=l Ounce. 
16 Ounces=il Pound. 

Avoirdupois Weiglit. 

16 Drachms:=:l Ounce. 
16 Ounces^l Pound. 
28 Pounds=l Quarter. 

4 Quarters=l Hundredweight. 
20 Hundredweights! Ton. 

HOPPER BALE BREAKER. 

This machine is made in the Unite< 
States bj'- Messrs. Howard and Bullough 
of Pawtuclcet, Rhode Island. 

Its work is to brealc the cakes of cot 
ton, which are pulled from the newlj 
opened bales, without damage to th( 
fibres. 

It mixes waste with cotton evenly. I 
is a great improvement to opening oi* 
breaking the cotton by hand, and saves 
a great amount of labor, as one of these 
machines will open a lull sized bale of 
American cotton in from 6 to 10 minutes, 
or about 175,000 lbs. per week. 

AUTOMATIC FEEDER. 

The Automatic Feeder feeds the cotton 
evenly to the opener. 

The cotton is fed into the hopper and 
carried by a spiked lattice or apron to 
the Stripping Comb. The Stripping Comb 
knocks back the surplus cotton taken up 
by the vertical spiked lattice, so in case 
a heavier feed is required, the stripping 
roll is set further away from the lifting- 
apron, and if a lighter feed is required 
44 



it is set nearer, or the lifting apron may 
be made to run slower or quicker to 
feed heavy or light. 

The feed to the opener is controlled by 
a wood condensing roll. 

See that there is no slippage of the 
apron, and keep the machine clean, re- 
moving the sand, seeds, and dirt regu- 
larly. 



OPENER. 

Its duties are to open and clean the 
cotton and take out foreign matter. 

Some makes cut or chop the cotton and 
cause trouble. 

The revolutions of an 18 inch rigid 
beater are about 14.50 per minute; and 
a porcupine beater 550 R. P. M. 

The distance of the beater blades to 
the feed roll for working medium Ameri- 
can cotton is 5/16 of an inch. 

The beater blades should be sharp, but 
not sharp enough to cut the cotton. 

They should give the cotton a sharp, 
solid blow to knock out the dirt. 

If the beater knocks out the cotton in 
bunches there is not sufficient weight 
on the feed roll. 

If the laps vary much in weight the 
evener and feed roll are not working cor- 
rectly. 

The production of one of these ma- 
chines is anywhere from a 1000 to 7000 
lbs. per day. 



45 



BREAKER LAPPER. 

The two machines mentioned before 
are generally connected to this machins 
In various ways. 

The Feeder and Opener are placed in 
another room and connected by conduct- 
ing trunks, or they can be directly con- 
nected to the Breaker Lapper. 

For stock 1% to 1% inch, a good speed 
for porcupine beater is 550 R. P. M. The 
rigid beater 1300 R. P. M. and the fan 
1100 R. P. M., but these vary greatly 
according to the cleanliness of the cotton. 

Pay great attention to the setting of 
the bars. 

Set bars about i/^ inch and note re- 
sults. If you make too much waste close 
them, and if the dirt is coming along 
with the cotton open them. 

When working Sea Island spread the 
bars and run the rigid beater about 1100 
R. P. M. But much depends on whether 
you are short of laps in card- room. 

The same applies to this machine in 
reference to the beater and feed rolls, as 
mentioned in the opener. 

A good speed for the fan with the other 
speeds given is 1100 R. P. M. But this 
depends largely on how they are dealing 
with the cotton in blowing it on the 
screens or cages. A good plan is to 
place a triangular piece of wood the 
whole length of the screens and near to 
where the screens meet, and divide the 
air current. This stops the cotton from 
being blown at the junction of the 
screens and prevents thick and thin 
places in the lap; it also, to a great ex- 
tent, does away with splitting or licking 
laps. 

See that the fan blows the cotton 
evenly on the screens or the lap will 
not be parallel from end to end, 
46 



FINISHER LAPPER. 

This machine is designed to double the 
laps from the breaker lapper, and in 
this way get a more even lap. 

The beaters and fans have been dealt 
with on tlie Breaker Lapper and Opener. 

The Pin Beater has not been mentioned. 
It is a beater with pins set in the 
blades, and for long staple cotton it 
works splendidly. 

For Sea Island a pin beater would do 
well at 1100 R. P. M. and the fans 1300. 

Always be well equipped for fires in 
the picker room. 

Keep the room and machines clean. 

The laps should be cylindrical, solid 
throughout, and have perfect salvages. 



Calculations on Lappers. 

To find speed of beater: — 

Speed of line shaft 230 R P. M. Pulley 
on line shaft 36 inches, which drives a 
20 inch pulley on counter shaft, and an- 
other pulley on counter shaft 28 inches 
drives the pulley on the end of the beater 
shaft, which is 8 inches. 

Rule: — Multiply the driving pulleys and 
the revolutions of the line shaft together, 
namely, 230, 36, and 28. 

Then multiply the driven pulleys to- 
gether, which are the 20 and the 8, and 
divide the drivers bj^ the driven, then 
you have the revolutions of the beater 
per minute. 

230X36X28=231840 



20X8 = 160 
231840h-160=1449 R. P. M. of beater. 



The fan is driven from the beater 
shaft; so for example take a pulley on 
the beater shaft 6 inches, driving a pul- 
ley on the fan shaft 8 inches diameter,' 
What vi^ould be the speed of the fan? 

Rule: — The beater revolves 1449 R. P. 
M. Multiply this by 6 and divide the 
product by 8. 

1449X6=8694 



8694^8=1086 R. P. M. of fan. 



To find percentage of waste: — Multiply 
weight of droppings by 100 and divide by 
weight of production and droppings 
added. 

To find the Hank Lap: — 

We must remember that 840 yards 
make one hank and 7000 grains 1 lb. So 
if 840 yards of lap, sliver, or yarn weigh 
7000 grains, or 1 lb., then the counts must 
be Is. or one hank to the pound. If 840 
yards weigh 1000 grains, then the sliver 
or yarn would be 7s. because we would 
require 7 times 840 yards to make 7000 
grains or 1 lb. 

Find the Hank of a 12 ounce lap. 

Divide 7000 grains by 840. This gives 
8.33, which means each yard weighs 8.33 
grains. Now find how many grains there 
are in 12 ounces. There are 7000 grains 
in 1 lb. and there are 16 ounces in 1 lb. 
By dividing 7000 by 16 we get to know 
how many grains in an ounce; 7000 di- 
vided by 16 equals 437i/^ grs. in an ounce. 
Then multiply 12 by 437 1/4 and we get 

4S 



5250 grs. in 12 oz. Now divide the grains 
per yard (8.33) by 5250 and you have the 
Hank Lap. 

8.33^5250=.00158 hank of lap. 



CARDING. 

Settings. 

Set Doffer, Licker-in, and Flats as near 
to the Cylinder as possible without touch- 
ing. 

Feed Plate to Licker-in 12/1000 of an 
inch. 

Cylinder screen to Cylinder 20/1000 of 
an inch. 

Licker-in knives to Licker-in 12/1000 of 
an inch. 

Back knife to Cylinder 15/1000 of an 
inch. 

Front knife plate to Cj^linder (lower 
edge) 15/1000 of an inch. 

The above settings are for a medium 
heavy production. 

When carding light, set all setting parts 
as near as possible without touching. 



Draft between Lap Roll to Calender 
Roll:— 

Multiply Lap Roll gear (59) by Feed 
Roll gear (154) and side shaft Bevel gear 
(32) and Doffer gear (180) and diameter 
of Calender roll 4 inches. 

Then multiply the following gears to- 
gether: Lap Roll driving gear (21). Draft 
bevel gear (20). Side shaft gear (26). 
Calender gear (28), and Diameter of Lap 
Roll 6 inches. 



8 3 

22 X&i 9 

59 X l&JL X 3^ X 1^0 X ^ = 1038 



^X X 2p X ^0 X ^8 X ^ = 91- 
7 13 J ^ 

10384^S1=113 draft. 
To find constant for draft: 
Use the same gears as when findin 
the total draft, but leave out the draf 
gear (20). 

10 
23 16 3^ 

59 X m y: 3;^ X X^^ X ^ = 207680 
?1 2^ X i^ X ^ = 91 

7 13 J 

207680^91=2282 constant. 

To get draft gear, divide the constant 
by the draft required. Say, for example, 
we want a gear to put in 113 of draft. 

2282 (constant) divided by 113 (draft) 
equals 20. Then a 20 draft gear would 
give 113 draft. 

Length of Clothing required to cover 
cylinder and doffer. 

Diameter of cylinder 50 inches, and 
width of carding surface 40 inches, would 
reqviire 268 feet of clothing, 2 inches wide. 

A cylinder 50 inches diameter, and 45 
inches wide, would require 297 feet of 
clothing 2 inches wide. 

A doffer 24 inches diameter, and 40 
inches wide, requires 172 feet of 1% inch 
clothing. 

A doffer 27 inches diameter, and 40 
inches wide, requires 194 feet of clothing 
iy2 inches wide. 

50 



A doffer 27 inches diameter, and 45 
inches wide, requires 218 feet of 1% inch 
clothing. 

SLIVER LAP MACHINE. 

This machine converts the sliver from 
the card into a lap to be put on the rib- 
bon lap machine or on the comber direct. 

There are usually 14 to 20 slivers taken 
in behind to form the lap. 

A small draft of about 1.5 is generally- 
put in here. 

RIBBON LAP MACHINE. 

This machine dispenses with the first 
drawing frame. It doubles the laps (gen- 
erally six) from the sliver lap machine, 
and makes an evener lap for the comber. 

The draft is governed by the number 
of laps being doubled; it generally runs 
from 4 to 6 of draft. 

Spread the rolls according to the weight 
of laps behind, say from Vs to % of an 
inch wider than the staple of cotton 
being worked. 



COMBER. 

This machine takes out the short fibres, 
neps, and leaf by the needles in the half- 
lap combing the front ends of the fibres, 
whilst they are held by the nippers, and 
the top comb combing the rear ends by 
having the fibres drawn through it by 
the fiuted segment and the detaching 
rolls. 

This process makes a lot of waste, 
generally from 16 to 22%, but it makes 
a stronger, evener, and cleaner yarn, with 
a better lustre, as it combs the fibres 
parallel. 

51 



A single comber gives from 80 to 9! 
nips a minute. 

A good plan when starting a new ma 
chine is to commence slowly, then grad 
ually increase in speed untfi you find th( 
quality of the work deteriorating; thei 
stop right there. This applies to all ma 
chines. 



Roller Varnish Receipt. 



1 lb. Gelatine Glue. 
12 oz. Burnt Senna. 

2 quarts of Acetic Acid. 
4 oz. of Red Lead. 

1 oz. of Origanum. 



Comber Setting. 



Feeds at 5 index 

Nipper knife touches 

cushion plate 9 to 9 1^ index 

Leather detaching roll 

touches segment ... 6% index 
Leather detaching roll 

leaves segment 9% to 9% index 

Delivery roll delivers. 6i/4 to GV2 index 

Top comb working 5 index 

Cushion plate to 

need es on halt - lap. .18 to 21 gauge 
Stop screw to nipper 

stand 14 step gauge 

Cushion to detaching 

roll 114 finger gauge 

Feed roll to detaching 

roll 1 13/16 finger gauge 

Top comb to segment.l8 to 21 gauge 
Angle of top comb 28 to 32 

These settings vary according to length 
of staple, but for a 2.50 gr. lap. Egyptian 
the above settings are good. 

52 



Comber. 

Draught from Lap Roll to Calender 
delivery roll: — 

Multiplj^ the following driving gear 
together: — Lap roll gear 47. Bevel gear 
55. Diagonal shaft gear 22. Feed Roll 
gear 38. Notch or star gear 5. Cylinder 
shaft gear 25. Front cross shaft gear 50. 
Gear 45. Front Roller gear (on opposite 
end of shaft) 20, and diameter of calender 
roll 2%", which we will call 11, as there 
are 11 quarters in 2%". 

Then multiply the following gears to-" 
gether: — Gear between Lap gears 37. 
Gear on diagonal shaft 20. Feed Roll 
gear 22. Change gear 16. Feed Peg 1. 
Front cross shaft gear 25. Gear on stud 
45. Roller gear 42. Calender shaft gear 
43. Diameter of lap roll 2%", or 11 quar- 
ters. 

Then we get t'he following: — • 

47X55X22X38X5X25X50X45X20X11 

37X20X22 X16X1X25X45X42X43X11 

=22.97 draft. 

or alm.ost a draft of 23 we get by mul- 
tiplying the gears above the line, then 
multiplying the gears below the line, and 
dividing the product of the top line by 
the product of the bottom line. 



An easy way to get the draft is to 
mark a yard of the lap behind, putting 
a mark on the back of the comber. Set 
the first mark on the lap even with the 
mark on the machine, then break the 
sliver at the coiler. 

53 



start the comber, and when the yard 
of lap has gone to the stationary mark 
on the comber, again break the sliver at 
the coiler, and measure it. If there are 
27 yards delivered for 1 yard fed at the 
back, then we have a draft of 27. 



To find amount of waste, break the 
sliver at the coiler and clean all the waste 
from behind the machine, run the comber 
a short time, break the sliver again and 
weigh the sliver that has come through 
also the waste made during this short 
time. 

Suppose the sliver weighs 60 penny- 
weights and the waste weighs 10 penny- 
weights. 

Multiply the weight of waste by 100 
and divide by weight of sliver and waste 
added. 

60 100 
10 10 



70)1000 



14.28 percentage of waste. 



There is a weighing-machine made 
which gives the percentage of waste 
made, on a quadrant. 

DRAWING FRAME. 

As the name implies, this machine 
makes the slivers more uniform and the 
fibres more parallel by drawing them, 6 
to 8 slivers from the card or comber 
being fed behind, and drafted so as to 
come out in front of the frame about the 
weight of one sliver fed behind. 

54 



Suppose there are 6 slivers fed behind, 
each weighing 60 grains, and there is a 
draft of 6 in the rollers. The one sliver 
in front of the frame will remain a 60 
grain sliver. 

Constant for Draft between Back Front 
Rolls. 

Multiply Back Roll gear 70 by Crown 
gear 100, and by diameter of Front Roll 
11 for a dividend. 

. Then multiply Front Roller gear 25 by 
diameter of Back Roll 9 for a divisor. 

70X100X11=77000 

25X9 = 225 
77000^22.5=342 Constant. 

Divide Constant by draft, and this will 
give Draft Change gear. 

342 Constant divided by 6 Draft=57. 
57 Draft gear to give 6 of a Draft. 

Draft from Back Roll to Bottom Calen- 
der Roll. 

Multiply Calender Roll Compound gear 
32, by Crown gear 100, by Back Roll gear 
40, and by diameter of Calender Roll 16, 
for a dividend. 

Then multiply gear on Calender Roll 
24, by Compound gear 45, by Draft gear 
30, and by diameter of Back Roll 11, for 
a divisor. 

32X100X40X16=5120 



24X 45X30X11= 891 
5120h-891=5.74 Draft. 



The above figures were cancelled. 
Note that the figures 16 and 11 are used 
for the Calender Roll and Back Roll. 
55 



The Calender Roll is 2 inches diameter* 
and the Back Fluted Roll 1% inches. 

These rolls are reduced to eighths of an; 
inch. There are 16 eighths into 2 inches, 
and there are 11 eighths into 1% inches. 

This rule is also used in the Draft from 
Back to Front Roll. Back Roll is IVs anql 
the Front Roll 1%, so we use the figures 
9 and 11. 



Roller Varnish Receipt. 

1^ lb. of Gelatine r,iue. 
V4 lb. of Pulverized Glue. 

1 quart of Acetic Acid. 

1 tablespoonful of Origanum Oil. 

1 teaspoon ful of Brown Sugar. 



56 



FLY FRAMES. 

Slubbing, Intermediate, Roving and Jack 
Frames. 

These machines are built somewhat 
similar, excepting the slubber, which has 
no creel, it being the first machine after 
the Drawing Frame. The cans of sliver 
are placed behind the slubber and wound 
on a bobbin, whilst an actual twist is put 
in here, for the first time, so at this ma- 
chine the spinning really commences. 
Before, the Picker, Card and Comber 
have cleared the cotton of impurities and 
taken out short fibres. The Drawing 
Frame has made the slivers uniform or 
even, and now we want to diminish the 
slivers, and make the fibres still more 
parallel by drafting as fine as required, 
and as even as possible to prepare them 
for the Mule or Ring Frame. For the 
purpose of making the roving even, it is 
doubled at the Intermediate, Roving, and 
Jack Frames. 

Jack Frames are only used where fine 
counts are spun, as the bobbins required 
must be small and liglat, to draw off 
easily at the Mule or Ring Frame, with- 
out breaking the roving. The Jack 
Frame also makes the drafts smaller in 
the other Frames. For without this 
Frame it would be quite a task to make 
a 25 Hank Roving from an ordinary sliver, 
without having excessive drafts in the 
Slubber, Intermediate, and Roving 
Frames, and this wovild make roller-laps 
by the drafts being too high, and conse- 
quently waste. 

57 



The bobbins are run by the cone drums, 
which act exactly as tlie quadrant does 
to the spindle on the Mule. 

As the Bobbin becomes larger in 
diameter, and the rolls are delivering the 
same amount of roving, the Bobbins must 
run slower to wind on the roving deliv- 
ered. To do this the Cone-belt is inoving 
a little at evei-y change of the rail, just 
as the quadrant chain on the mule is 
shortening until the cop reaches the body 
or thickness. 

This, of course, is a Frame with a 
bobbin lead, or, in other words, v/hen the 
speed of the bobbin is in excess of the 
flyer, but when it is a Flyer Lead, the 
speed of the flyer is in excess of the 
bobbin, and so winds the roving on the 
bobbin. 

Then after doffing the bobbins run 
slowly and gradually increase in speed 
until the time for doffing. 

Constant for turns per inch, on Slub- 
bing Frame: — 

Multiply Front Roll gear 120, by Top 
Cone gear 35, by Driving Shaft gear 44 
and by Spindle bevel gear on shaft 50 
for a dividend. 

Then multiply gear on Cone Drum 
shaft 64, by gear on the end of Spindle 
shaft 44, by gear on the bottom of Spindle 
25, and Circumference of Front Roll l'/4 
inches or equal to 3.92. 

120X35X44X50 =525 



64X44X25X3.92=15.68 



(The above figures have been cancelled 
before being multiplied.) 

58 



525^15.68=33 Constant. 

Divide Constant by turns per inch re- 
quired, and it will give you Twist gear. 

Suppose you w'ant to put in .777 turns 
per incli. Divide the Constant 33 by .777. 
(All the sevens being decimals we must 
add three ciphers to the 33.) (See Deci- 
mals.) 

33.000^.777=42 Twist Gear. 



Constant for Draft in Slubbing Frame: 

Multiply Back Roll gear 60, by Crown 
gear 90, and by diameter of Front Roll. 
11/4 inches (or 10 eighths) for a dividend. 

Then multiply Front Roller gear 24, by 
diam.eter of Back Roll 1 inch (or 8 
eighths). 

60X90X10=54000 



24X8 = 192 
54000^192=281 Constant. 

Constant divided by draft gives Draft 
gear. 

281 (Constant) divided by 5 (Draft)=56 
Draft gear. 

To find Lay or Lifter Gear. 

Suppose a 6 hank-roving requires a 14 
lay gear, what lay gear will a 4 hank 
roving require? 

Rule: — Square 14 by multiplying 14 by 
14, then multiply the product by 6 and 
divide by 4, and get the square root of 
the quotient. 



59 



Example: 



4)1176 

VI) 294(17 lay gear required. 
1 

27) 194 
189 



Another way to find Lay Gear, which 
is far simplier than the rule before 
given : — 

Multiply the 14 by the 6 hank roving 
and divide by the 4 hank roving, add the 
14 to the answer and divide by 2. This 
gives lay gear. 



Example : 



14 



4)84 



2)35 



17.5 lay gear. 
17 Lay or Lifter Gear required, 
GO 



To find change for Twist Gear: 



Suppose you are making a 6 hank rov- 
ing with a 30 twist gear on. What twist 
gear would you require to make a 4 hank 
roving? 

Rule:— Square the 30 twist gear. (This 
means multiply 30 by 30.) 

Then multiply by the hank roving you 
are making 6, and divide by the hank 
roving you are going to make 4, and the 
square root of the answer is the twist 
gear required. 



Example: 30 twist gear 

30 

900 

6 hank you're making 



Hank to make 4)5400 



V36) 1350(36.7 twist gear reqd 
1296 



727)5400(7 
5089 

.7 or almost 37 Twist Gear required. 



Another and easier rule. 

Multiply the 30 by 6 hank roving and 
divide by 4. Then add the 30 to your 
answer and divide by 2. This will give 
you Twist Gear required for a 4 hank 
roving, if a 6 hank roving requires a 30 
Twist Gear. 

61 



Example: 30 twist gear 

6 hank you're making 



Hank to make 4)180 



45 

30 twist gear added 



2) 75 

37 twist gear required. 



To find Tension or Rack Gear: 



Suppose you are making a 6 hank rov- 
ing with a 30 tension gear. Wliat ten- 
sion gear would a 4 hank roving require? 



Rule: — Multiply the tension gear on, by 
the square root of tlie hank roving being 
made, and divide by the square root of 
the hank roving j'ou are going to make. 

Example: Square Root of 6 is 2.4. 
30 tension gear 
2.4 square root of 6 

120 



Square root of 4=2)720 

36 tension gear reqd. 

All the calculations given in regard to 
the Slubber apply exactly the same to the 
Intermediate, Roving and Jack Frames. 



To find Turns per inch required: — 
American and Low Egyptian. 

Slubber, Square Root of H. R. multi- 
plied by 1.16. 

Intermediate, Square Root of H. R. 
multiplied by 1.16. 

Rover, Square Root of H. R. multiplied 
by 1.25. 

Jacks, Square Root of H. R. multiplied 
by 1. 



Good Egyptian and Sea Island. 

SlublDer, Square Root of H. R. multi- 
plied by .7. 

Intermediate, Square Root of H. R. 
multiplied by .78. 

Rover, Square Root of H. R. multiplied 
by 1.1. 

Jacks, Square Root of H. R. multiplied 
by .95. 

These tvs^ists are changed according to 
the quality of the cotton and the condi- 
tion of the weather. 



To find the Draft Change Gear to put 
in a draft of 5.5 with the following 
gears : — 

Front Roll Gear 30 teeth. 
Crown Gear 100 teeth. 
Back Roll Gear 60 teeth. 
Diameter of Back Roll 1% Inches. 
Diameter of Front Roll 1^/4 inches. 

Multiply Front Roll Gear 30, by 
diameter of Back Roll l^/^ inches or 9 
eigths, and by Draft required 5.5. Take 
these for a divisor. 

63 



Then multiply Crown Gear 100 by Back 
Roll Gear 60 and diameter of Front Roll 

114 Inches, or 10 eights. 

Take these for your dividend. 
Example : 

lOOX 60X10=60000 

30X5. 5X 9=1485 
60000^1485=40 Draft Gear. 



We are making a 8 hank roving with 
a 31) draft gear. What Draft Change Gear 
is required to make a 6 hank roving? 

Rule: — Multiply Change pinion on, (30) 
by hank roving being made (8) and 
divide by hank roving (6) we are going 
to make. 
30 
8 

6)240 

40 draft change gear required. 



To find turns per inch on Interme- 
diate: — 

Multiply gear on driving shaft 52, by 
Spindle shaft bevel gear 57, and by Top 
cone gear 55, and by Front Roll Gear 140. 
These gears taken for a dividend. 

Then multiply End Spindle Shaft gear 
50, by Spindle gear 25, and by Twist 
gear 52, and by gear at the opposite end 
of cone 78, and by diameter of Front Roll 
11/4 inches or 3.927. These gears use for 
a divisor. 

64 



52X57X55X140 =1463 

50X25X52X 78X3.927=1276.275 
(The above numbers were cancelled be- 
fore multiplied.) 

1463 — 1276.275=1.14 Turns per inch. 

To get a constant for Twist Gear: — 

Rule: — Proceed exactly as in the exam- 
ple given to find turns per inch, but leave 
out the Twist Gear 52. 

Example : 

52X57X55X 140=22822800 



SOX 25 X 78 X 3.927=382882.500 
22822800-^382882.5=59 Constant. 
59 Constant divided by 1.14 Turns per 
Inch equals 52 Twist Gear. 



These Twists and Drafts apply also to 
Rover and Jack Frames. 



WRAPPING OR SIZING SLIVERS, ROV- 
INGS, AND YARNS. 

In finding the Hank of Slivers weigh 
a yard of Sliver, and suppose it weighs 
58 grains, divide this in 8.33. 

8.33^58=.14 Hank Sliver. 

The reason for dividing one yard on 
sliver in 8.33 is because there are 8.33 
grs. to one yard of Is.: to get this divide 
7000 grains by 840 yards. 

7000-^840=8.33 grs. per yard. 
65 



1 



Wrapping or Sizing Roving. 

Wrap 12 yards of Roving, and divide 
weight in grains in a hundred. 

Suppose 12 yards weigh 50 grains. 

100-=-50=2 Hank Roving. 

The reason we divide the weight of 12 
yards into lOQ is because 12 are 1/70 part 
of 840 yards, or 1 Hank, and 100 is 1/70 
part of 7000 grs., or 1 lb. 



Wrapping or Sizing Yarn. 

Wrap or Reel 120 yards and divide the 
weight in grains into 1000. 

Suppose 120 yards or 1 Lea weighs 50 
grains. 

1000 divided by 50=20s Yarn or Counts. 

The reason for dividing the weight of 
120 yards into 1000 grains is that 120 yds. 
are 1/7 of 840 yds. and 1000 grs. are 1/7 
of 7000 grs., or 1 lb. 



SETTING ROLLS. 

It is very difficult to give a fast rule for 
the Setting of Rolls, as the Front Roll 
running slowly, or at an excessive speed, 
also the feed being heavy or light, govern 
the settings to a great extent. 



Drawing Frame Rolls. 

For Combed stock set Front and 2nd 
Roll 1/16 of an inch further apart from 
centre to centre than the length of the 
staple of the cotton being worked. And 
from centre of 2nd Roll to centre of 3d 
Roll set Vs of an inch further apart than 
length of staple. And from centre of 3d 
Roll to centre of Back Roll set 3/16 of an 
inch further than length of staple. 



Drawing Frame. 

Suppose, for example, you are work- 
ing combed stock 1% inch staple. 

Distance from centre to centre of Front 
and 2nd Roll 1 7/16 of an inch. From 
centre to centre of 2nd and 3d Roll 1 1/2 
inches. From centre of 3d Roll to centre 
of Back Roll, set 1 9/16 of an inch. 

For Carded work you may set the rolls 
% of an inch. Front and 2nd % of an 
inch, 2nd and 3d and % of an inch 3d 
and Back Rolls, further apart than length 
of staple. 

Note result after setting rolls, and if 
the sliver comes through not properly 
drawn, or in tufts, spread the rolls a little 
more. 



SLUBBER ROLLS. 

Set from centre of Front Roll, to centre 
of 2nd or middle roll, 1/16 of an inch 
wider than the staple you are working, 
and from centre of middle roll, to centre 
of Back Roll % of an inch longer than 
staple. 



INTERMEDIATE ROLLS. 

Set these similar to Slubber Rolls. 



ROVER AND JACK FRAMES. 

Set Front and Middle Roll a little fur- 
ther apart than length of staple, from 
centre to centre, and from centre of mid- 
dle roll to centre of Back Roll Vs of an 
inch. 

67 



MULE AND RING FRAME. 

Set Front and Middle Roll from centra 
to centre slightly Wider than staple. 

Always take in consideration, whei 
setting rolls, whether the feed is heav] 
or light. For a heavy feed, set rolls furJ 
ther apart, for a light feed set nearer. 

Watch your drafts when setting rolls 
If a small draft, set your rolls furtht 
apart, and, if a large draft, set rol 
nearer. 

Look to your Roving when setting roWi 
If it is hard twisted, set the rolls furth€ 
apart. If the roving is soft, set near. 

With Self-weighted rolls on Fly Framesr 
set Back and Middle Rolls a little further 
apart. 

Never have Top Leather Roll the same 
diameter as the fluted roll, for if they 
are, the leather will become fluted. 

Keep the leathers on the rolls in good 
condition. 

Loose Boss Front Rolls are best. 



Varnish for Drawing Frame Rolls. 

11/^ lbs. Fish Glue. 

V^ lb. of Gum Arabic. 

1/4 lb. Powdered Alum. 
2 lbs. Acetic Acid. 
4 lbs. Water. 

Add together, dissolve over slow fire, 
and when cold, it is ready for use. 



Circumference of Rolls. 

1 inch diameter, circumference is 3.1416. 

1 1/16 inch diameter, circumference is 
3.3379. 

1 1/8 inch diameter, circumference is 
3.53. 

1 3/16 inch diameter, circumference is 
3.73. 

1 1/4 inch diameter, circumference is 
3.92. 



69 



SELF-ACTING MULES. 






Good Drafts for Mules spinning Ameri- 
can Cotton range from 7 to 10, but these 
are often exceeded. In spinning good Sea 
Island Cotton, 14 of a draft is common. 

Suppose you were going to spin 50s. 
yarn from a 10 hank roving double. The 
10 H. R. being double, would be twice as 
heavy, so it would equal a 5 H. R., and 
you require what is termed 10 of a draft, 
or, in other words, draw the 5 H. R. ten 
times finer. You see this by saying 10 
times 5 are 50. 



To find Draft Gear, to give a draft 
of 10. 

We will suppose you have a Back Roll 
gear on 54. Multiply this by Crown Gear 
120, and by diameter of Front Roll 1 inch. 
Take these for a dividend. 

Then multiply Front Roll gear, which 
we will suppose to be 18, by the Draft 
required 10, and by diameter of Back 
Roll 1 inch. Take these for a divisor. 



Example : 

B.R.G. C.G. D. ofF.R. 

54 X 120 X 1 =6480 

10 X 18 X 1 =180 
Draft. F.R.G. D. of B. R. 
6480-^180=:36 draft gear required. 
70 



If the Front Roll diameter is 1 1/16 of 
an inch, and the Back Roll 1 inch, reduce 
them to sixteenths. There are 16 six- 
teenths in one inch, so there must be 17 
in 1 1/16 inch. 

Place your terms thus: 

54X120X17=110160 



lOX 18X16= 2880 
110160^2880=38 draft gear required. 



If the diameter of the Front Roll is 1^ 
inch, reduce to eights. There are 9 eighth 
in 1% and 8 eights in 1 inch. 

54X120X9=58320 



lOX 18X8=1440 
5832:)^1440=40 draft gear required. 

To find Constant for Draft. 
Rule: — Proceed exactly as when finding 
Draft Gear, but leave out the draft. 



Example: 



54X120X1=6480 



18X1 = IJ 
6480^18 = 360 Constant. 



71 



The Constant divided by the Draft re- 
quired will give you Draft Gear. 

360 (Constant) divided by 10 (Draft re- 
quired)=36 Draft Gear. 

Suppose you require 9 of a draft. 

360 divided by 9 equals 40 Draft Gear. 

If you take the rule given before, the 
Counts vi'ould come a little lower than 
50s. The reason for this is that 1/15 is 
generally taken up with the twist, which 
would make the numbers of the yarn 
heavier. 

You must also watch the drag or gain 
in the carriage, for this is equal to putting 
in more draft. For if the Rolls only 
deliver 62 inches and the Stretch of the 
Mule is 64 inches, you are drawing the 
yarn finer. 

A good rule to find the Numbers of the 
Yarn, from the hank roving, is the fol- 
lowing: — 

We will suppose the Roving in the 
Creel is 8 hank doubled. This would equal 
4 hank, and you are going to put in 9 
of a draft, and the Front Roll delivers 62 
inches, and the length of stretch is 64 
irches. Now find the Counts or Numbers 
of the Yarn. 



Rule:— Multiply the H. R. 4, by the 
Draft 9, and the length of stretch 64 
inches, and divide the product by the 
length delivered by the Front Roll 62 
inches. Then deduct 1/15 from your 
answer for twist and you will have the 
Counts or Numbers of the Yarn. 



72 



Example : 

4 H. R. 
9 draft 



36 

64 L. of stretch 



144 
216 



L..D. byF. R. 62)2304(37.16 
186 

444 
434 

100 
62 

380 
372 



Taken up by twist 1/15)37.16(2.47 



7.1 
6.0 



1.16 
1.05 



37.16 
2.47 

84.69 yarn you get. Answer. 
73 



To find the Draft Gear, from one nui 
ber of yarn to another, without changii 
Ro-ving: — 

Suppose you have on a 45 Draft Gea 
and spinning 40s yarn, and you wish 
make 45s yarn out of the same roving. 

Rule: — Multiply the 45 Draft Gear you 
have on, by the numbers you are spinning. 
40s, and divide the product by the num- 
bers you wish to spin 45s. 
45 
40 

45)1800(40 draft gear required for 45s yarn 

180 



To find the Twist or Turns per inch re- 
quired for the Numbers of Yarn you are 
going to spin: — 

Suppose you are going to spin 36s Fill- 
ing. 

Rule: — Multiply the standard used for 
filling, which is 3.25 or 314,, by the square 
root of the numbers you are going to 
spin. 

Example: — Square root of 36 is 6, and 
3.25 multipliefd by 6 equals 19.50 or IdVz 
turns per inch for 36s filling. 



When spinning warp yarns on mules: — 

Multiply square root of Counts by 3.75. 
This gives turns per inch required. 



74 



i The 3.25 and 3.75 are often left and 
standards of the overseer's used, as much 
depends on the quality of the cotton, and 
whether a hard or soft twisted yarn is 
required. 

Sometimes a standard of 2 is used for 
very soft hosiery yarn. 

This makes quite a difference to the 
turns per inch for the same numbers of 
yarns. 

Take for example, you are spinning 16s 
hosiery yarn and using a standard of 2. 
You would say the square root of 16 is 4 
and multiplied by 2 equals 8 turns per 
inch required to spin very soft hosiery 
yarn, and in using the standard 3.25 we 
get 13 turns per inch for exactly the same 
numbers of j^arn. 



To find Constant for Twist, or Turns 
per inch on Messrs. Hetherington's Rim 
at Back, or Ordinary Mule: — 

Rule: — Multiply Front Roller Box Bevel 
gear 38, by gear 35, and by gear 58, and 
diameter of Rim Pulley IS inches, and 
diameter of cylinder 6 inches, or 97 six- 
teenths. Take these for a dividend. 

Then multiply the bevel gear 17, by the 
gear 28, and by diameter of Cylinder 
Pulley 12 inches, and by the diameter of 
spindle whirl % of an inch or 13 six- 
teenths, and circumference of Front Roll 
3.1416. 

38X35X58X18X97 = 134686440 

17X 28 X 12 X 13 X 3.1416=233282.6496 
134686440.0000^233282.6496=577 constant. 



75 



Note. — Having 4 decimals in the divisoi 
we must add 4 ciphers to the dividend. 



35 



190 
114 



1330 
58 



10640 
6650 



77140 
18 



617120 
77140 



1388520 
97 



9719640 
12496680 



233282.6496)1346864400000(577 constant. 
11664132480 



18045115200 
16329785472 



17153297280 
16329785472 



3.1416 
13 



94248 
31416 



408408 
12 



4900896 

28 



39207168 
9801792 



137225088 
17 



960575616 
137225088 



233282.6496 



Note. — The writer would refer you to 
Arithmetic (Cancellation), as this exam- 
ple could be shortened considerably by 
cancelling the numbers. 



The turns per inch required to be put 
in the yarn, divided into the Constant 
577, give you the size of Speed Gear. 

Suppose you want 20 Turns per inch. 

Example: 577 divided by 20 equals 28 
Speed Gear at the end of Rim Shaft. 

The gears 38, 17, 35, and 28 are not 
generally changed, but the gear 58 is a 
change gear. With a 40 gear instead of a 
58, the Constant is 398. 

Note. — That 97 is used for diameter of 
cylinder, and 13 for diameter of whirl. 

77 



The reason is that we want to add 1/16 
of an inch for thickness of spindle band, j 
To do this reduce the cylinder to six-^ 
teenths of an inch. The cylinder being 6' 
inclies diameter, and there are 16 six- 
teenths in 1 inch. Then multiply 16 by 6 
and you get 96; add 1/16 for thickness of- 
band and you get 97. 

If there are 16 sixteenths in 1 inch, 
there must be 12 sixteenths in 3/4 of an 
inch whirl, and 1/16 added for thickness 
of band gives 13. This accounts for using 
the 97 and 13 for diameter of cylinder and 
whirl of spindle. 

Also note that when the Front Roll is 
1 inch diameter, the circumference is 
3.1416. This is used in the example. But 
suppose the Front Roll is 1 1/16 inches 
diameter, you must use 3.338 instead of 
3.1416. 

The reason is that the larger the 
diameter of the Front Roll the more it 
delivers at each revolution. Consequently 
you get less turns per inch with a thicker 
roll than you do with a thinner one when 
using the same gears. This rule applies 
to all mules. 



Constant for Drag or Gain of Carriages 
over Front Roll on J. Hetherington's 
Mule: 

Rule: — Multiply length of stretch 64 
inches, by Gear on Front Spindle 60, and 
by small Gear on Drag Gear 25, and by 
diameter of Scroll on Back Shaft and 
Band reduced to eights of an inch. This 
is the dividend. 



78 



Then multiply Back Shaft gear 75. by 
diameter of Front Roll reduced to eights 
of an inch. Diameter of Front Roll 1 
inch, or equal to 8 eights. 

r Example : 

I 64X60X25X45=4320000 



75X8 = 600 

432000-=-600=7200 constant. 



Divide Constant by length of stretch 
and Drag required and you get Drag or 
Gain Gear. 

Suppose length of stretch is 64 inches 
and you want a gain or drag of 3 inches. 
64" add 3" equals 67". 

7200^67=107 drag gear. 



To find Constant for Turns per inch on 
Messrs. Hetherington's Rim at Side 
Mule: 

Rule:— Multiply Front Roll Gear 90, by 
the gear 70, and by second change gear 
70, by diameter of Rim Pulley 18 inches, 
and by diameter of cylinder 6 inches, or 
97 (see Constant Rim at back). Then 
multiply the gear 45, by the gear 50, and 
by the diameter of the Cylinder Pulley 12, 
and by the diameter of the whirl % of 
an inch or 13 (see Constant Rim at back), 
and by circumference of Front Roll 3.1416. 

90X70X70X18X97 =142590 

45 X 50 X 12 X 13 X 3.1416=204.2040 

(The above numbers were cancelled be- 
fore being multiplied.) 

142590.0000-^204. 2040=698 constant. 



Constant divided by turns per incl 
give speed gear. 

The above Constant is witli a 70 secon( 
change gear on. With a 50 second chang 
gear, the Constant w^ould be 498.5. 

Suppose you want to put 20 turns pe 
inch in the yarn. 

698 (Constant) ^20=34 Speed Gear. 



To find revolutions of Spindle to on 
revolution of Rim: 

Suppose an 18 inch Rim is driving a 1 
Inch Cylinder Pulley, and a 6 inch Cylin 
der is driving a % inch vv^hirl on Spindle 

Rule: — Multiply 18 inch Rim by the 
inch cylinder for a dividend. Then mul 
tiply the 12 inch Cylinder Pulley by th 
% inch whirl, for a divisor. 

Example: 

18X 6 =108 



12X. 75=9.00 
108-^9.00=12 revolutions of spindle. 
Note that decimal 75 is used for the ^ 
whirl. The reason is that .75 is % of 100 
You can also place the terms thus: 
18X6X4=432 



12X3 = 36 
432-4-36=12 revolutions of spindle to on- 
of rim. 



If it is a % whirl place thus: 
18X6X8=864 



12X7 = 84 
864-4-84=10.28 revolutions. 



If it is one inch whirl: 
18X6=108 



12X1= 12 
108^12= 9 revolutions. 



To find Twist Gear when putting Twist 
in on the Catch or Latch. Commonly 
called "Head Twist" on Hetherington's 
Mule: 

Suppose you are going to put 30 turns 
per inch in, and the length of stretch is 
57 inches, and 3 inches added if you have 
roller motion on. This would equal a 60 
inch stretch. The diameter of cylinder 6 
inches and the spindle whirl % of an 
inch. Then there is the gear 20, driving 
the finger gear 68, and an 18 inch Rim, 
driving a 12 inch cylinder pulley. 

Rule:— Multiply length of stretch 60 
inches, by the turns per inch 30, and 
by gear 20 and diameter of cylinder pul- 
ley 12 and of whirl % of an inch. Take 
this for your dividend. 

Now multiply the finger gear 68 by the 
18 inch rim, and by diameter of cylinder 
6 inches. 



Example: 

60X30X20X12X3=1296000 



68X18X6X4 = 29376 
1296000^29376=44 Twist Gear required. 



81 



( Asa Lees & Go's Mule ) 



Draft Gear and Drafts are found 
actly as explained on the Hetheringtoi 
Mule. 

To find Constant for Speed Gear, oi 
Rim at Back: 

Rule: — Multiply diameter of Rim, whicl 
we will suppose to be 19 inches, by diany 
eter of cylinder 6 inches, and by Rolld 
Box Gear 48. Take this for a dividend. 

Then multiply Cylinder Pulley, whicii 
we will suppose to be 11 inches, by spiir 
die whirl % of an inch, and by Rim Pin' 
ion 22, and by Bevel Gear 24, which geamj 
with Roller Box Gear, and by circum 
ference of Front Roll 3.1416. 

Example: 

R C B C 

19 X 97 X 48 " = 88464 

11 X 13 X 22 X 24 X 3.1416=237203.3664 
C.P. S.W. R.P. B.G. F.R. 



88464-=-237203.3664— 372 constant. 



When dividing 88464 by 237203.3664 add 
4 ciphers to the 88464, as there are i 
decimals in 237203.3664, and the 3 figures? 
in the Constant are decimals (.372 Con- 
stant). 

The turns per inch required divided hy 
the Constant will give you Speed Gear. !* 

Note. — As the Constant is 3 decimals 

add 3 ciphers to your turns per inct, 

before dividing. j 

82 J 



Suppose you wanted to put in 30 turns 
per inch, and the Gears and Pulleys were 
the same sizes as we have used to find 
the Constant .372. 

Proceed as follows: [turns per inch. 

.372)30.000(80 speed gear required for 30 
2976 



.240 

Note. — In these examples there is no 
allowance for slippage of bands. 

Note.— Why the 97 and 13 are used for 
diameters of cylinder and spindle whirl 
is fully explained on the Hetherington 
Mule. 

In finding Constant for Speed Gear, you 
may use 7/22 instead of 3.1416, if the 
Front Roll is an inch diameter, and you 
get the same result, as: 

R. C. E.G. F.R. 

19 X 97 X 48 X 7 

.372 Constant. 



11 X 13 X 22 X 24 X 22 
C.P. S.W. R.P. E.G. F.R. 



If the Front Roll is 1 1/16 diameter 
place the terms as follows: 

19X97X48X16X7 



11X13X22X24X17X22 
or you can place them as follows, with 
exactly the same result, using 3.338 in- 
stead of 3.1416: 

19X97X48 



11X13X22X24X: 



If the Front Roll is IVs inches place asl 
follows : 

19X97X48X8X7 



11X13X22X24X9 X22 



19X97X48 



11X13X22X24X3.53 



If your mules are "Rim at Side" the^ 
Constant works out the same, the only; 
change being the two gears from the' 
Roller Box; on "Rim at Side" these gears 
are 60 and 30; on "Rim at Back" they are 
48 and 24. 



Constant for "Rim at Side" Mule with 
1 inch Front Roll. 

19X97X60X7 

:.372 Constant. 



11X13X22X30X22 



To find Twist Gear. 

Asa Lees's mule differs from the Del 
son and Barlow's and Hetherington" 
Mules, as the Worm for the Twist Gear 
is on the Cylinder Shaft and not on the 
Rim Shaft. So in finding the Twist Gear 
we haA'e not to deal with the Rim Pulley 
or Cylinder Pulley. 

Suppose the Cylinder is 6 inches and 
Spindle Whirl % of an inch, and the two 
Gears cast together, which generally are 
45 and 15. 

84 



Now suppose, for example, you are 
going to spin 100s and put in 30 turns 
per inch, and you wish to put % of the 
twist in as the carriage is coming out, and 
the other Vs whilst the carriage is on the 
latch or holding out catch, and suppose 
the length of the stretch is 57 inches, and 
a roller motion on delivering 3 inches, 
which makes the length of stretch equal 
to 60 inches. 

Rule: — Multiply the length of stretch 
with Roller Motion added, 60 inches, by 
the turns per inch 30, and by diameter of 
spindle whirl % of an inch and the gear 
15, which drives the Twist Gear. Take 
this for your dividend. 

Then multiply the diameter of Cylinder 
6 inches by the Worm Gear 45. Take this 
for divisor. 



E.xample: 

60X 30X 13 X 15=351000 



97X45 = 4365 
351000 -f- 4365=80 twist gear required. 



Constant for Twist Gear. 

Rule: — Proceed exactly as when finding 
Twist Gear, but leave out the Turns per 
Inch 30. 

Example: 

60X13X15=11700 



97X45 = 4365 
11700^4365=2.68 Constant. 
85 



Constant multiplied by turns per Incli 
will give Twist Gear. 

2.68X30 turns per inch=80 twist gear. 

Note.— There is no allowa.nce for slip- 
ping of bands. The overseer must make 
his own allowance with these calculations. 

Now we have got the Twist Gear, we 
want to put in % of the 30 turns per 
inch, until the carriage comes on the 
latch. 

Multiply 30 by 7 and divide by 8 and 
we have 26.22 turns per inch to put in 
during' outward run of carriage and the 
other Ys when the carriage Isj on the 
latch. 

Take the Constant .372 and divide the 
turns per inch 26.22 by it, and you get 
the Speed Gear. 

Example : 

.372)26.220(70 speed gear. 
26.04 



.180 



To change from, one Number or Count 
to another without changing speed gear, 
but to change Rim. 

Suppose you are spinning 50s with an 
18 inch Rim Pulley and you want to 
change to 45s by changing your Rim and 
keeping on the same Speed Gear. 

Rule: — Square the Rim Pulley 18 (that 
means multiply 18 by 18) and then mul- 
tiply this by the numbers you wish to 
spin 45s, and divide by the numbers you 
are spinning, and the square root of the 
answer is the Rim required. 



Example 




18 
18 








144 
18 






324 
45 






1620 
1296 






5 


0)14580(291 
100 








458 
450 






80 
50 




Square root 
for 45s. 


of 291 is 17. 


Rim required 


Here is another and simpler M'ay 
the Rim: 

Multiply the 18 Rim by 45 and 
by 50, add IS (Rim) and divide by 


to get 

divide 
2_ 


Example 


"18 
45 

90 

72 








50)810 










16 

18 








2) 


34 
17 


rim required 







To change from one Number to anoth< 
without changing your Rim, but i 
change Speed Gear. 

Suppose you are spinning 50s with a I 
Speed Gear, and you wish to spin il 
without changing your Rim. 

Rule: — Square the Speed Gear you hav 
on 55, and multiply by the counts or num 
bers you wish to spin 45, and divide b 
the counts you are spinning and ge 
square root of quotient. 



Kxample : 



275 

275 



50)136125(2722 
100 



361 
350 



112 
100 



125 
100 



Square root of 2722 is 52. 
required for 45s. 



Speed Gear 



Another and easier way to find one 
Speed Gear from another: 

Rule: — Multiply the Gear 55, by the 
counts 45s, and divide by the counts 50s, 
add the gear 55, and divide by 2. 

Example : 



53)2475 

49 
55 

2)104 

52 speed gear required. 

Note. — If the speed gear is a driver, 
instead of being larger for finer numbers 
it will be smaller. 

To find Drag Gear for 64 inch draw. 

Rule: — Multiply revolutions of Front 
Roll per stretch, which we will say for 
example are 20, by gear on Front Roll 
47, and by small gear on Drag Gear 25. 
Take these for a dividend. 

Then multiply turns of Back Shaft per 
stretch or draw 3.6 by Back Shaft Gear 
72. 

Example: 

20X47X25=23500 



3.6X72 =259.2 
23500.0^259.2=90 drag gear. 



To Find Shaper Gear. 

For 1% inch gauge of spindle, or, in 
other words, when the spindles are 1% 
inches apart, and the Shaper screw is 
Pitch 4. This meaning 4 threads to the 
inch. Then multiply the numbers you are 
going to spin by .7. 

Suppose you are going to spin 30s. 

Example: — 30 multiplied by .7= 210; 
strike off the cipher, as it was decimal 7 
you multiplied by. Then we get a 21 
Shaper Gear for 30s yarn. 

If your spindles in the mule are 1% 
inches apart, and a Shaper screw, pitch 
6, your Shaper Gear will be similar to 
the numbers you are spinning. Suppose 
you are spinning 40s, your Shaper Gear 
will be about 40. 

A fast rule cannot be given for the 
Shaper Wheel, as much depends on the 
weight on the Counter or under Faller, 
and the tightness of the winding, also 
the length of chase. If you have a long 
chase, the cop will be thinner than with 
a short chase, although you use the same 
Shaper Wheel. 



Production of Mule. 

Suppose a mule contains 90D spindles 
and it is running 4 stretches or draws a 
minute. Length of draw is 64 inches and 
3 inches added for roller motion equals 
67 inches. Find how many hanks per 
spindle, and the weight turned off in 56 
hours, deduct 3 hours for doffing and 
other stoppages, and the numbers of the 
yarn being spun is 40s. 

Rule: — Reduce the 53 hours to minutes 
by multiplying the 53 by 60, then multiply 

90 



this by draws per minute 4, and by length 
of draw 67. Take this for your dividend. 

Then multiply 840 (1 hank) by 36 inches 
(1 yard). 

Example: 

53X60X4X67=852240 



840X36 =30240 
852240-=-30240=28 hanks per spindle. 

Now we will find the weight per week. 

Rule: — Multiply the number of spindles 
900, by the hanks per spindle 28, and 
divide by the number of yarn 40s. 
Example : 

900 
28 



7200 
1800 



40)25200(630 lbs. per week. 
240 



120 

120 



To find the average Numbers or Counts 
being spun. 

Suppose you have spun 1000 lbs. of 80s, 
and 1000 lbs. of 70s, and 1500 lbs. of 50s, 
and 2000 lbs. of 40s, and 2000 lbs. of 36s, 
and 5000 lbs. of 28s. Now what is your 
average number or count? 

Rule: — Multiply each weight by counts 
and add them together. 

91 



Then a,dd all the weights sspun and 
divide the total into the weights multi- 
plied by counts. 

Example: 
Weight Spun. Counts. 



1000 


ms. 


multiplied 


by 


80 


equals 


80000 


1000 


n3s. 


multiplied 


by 


70 


equals 


70000 


1500 


lt3S. 


multiplied 


by 


50 


equals 


75000 


2000 


ItjS. 


multiplied 


by 


40 


equals 


80000 


2000 


rbs. 


multiplied 


by 


36 


squals 


72000 


5000 


lbs. 


multiplied 


by 


28 


equals 


140000 


12500 


517000 


517000-^ 


12500=41s 


average 


numbers of 


yarn. 















To find Constant for Speed Gear on 
D. & B. Mule. 

We will suppose the Rim Pinion is 19, 
driving a 48 gear on Compound, and the 
small gear on Compound 35, driving 
Speed Gear (which you omit when find- 
ing Constant for Speed Gear), and on 
opposite end of Side Shaft is a Bevel 
Gear 40, driving another Bevel Gear 40 
on Front Roller Catch Box. 

The Rim 18 inches diameter, driving a 
Cylinder Pulley 12 inches, and a 6 inch 
Cylinder, driving a % inch whirl on spin- 
dle, and Front Roll 1 inch diameter. 

Rule: — Multiply Bevel Catch Box Gear 
40, by gear on Compound 48, and diam- 
eter of Rim Pulley 18 inches, and diam- 
eter of Cylinder 6 inches. Take these 
for your dividend. 

Then multiply Bevel Gear on Side Shaft 
40, by small Gear on Compound 35, and 
Rim Shaft Pinion 19, and diameter of 
Cylinder Pulley 12 inches, and diameter 
of Whirl % of an inch, and Front Roll 
92 



1 inch (here you can use 7/22, or 3.1416 
for Front Roll). 
E\'ample: 

40X48X18X 6X 4X 7= 5805080 

40X35X19X12X 3x22=21067200 

5805080-=-21067200=:.275 constant. 

Note. — The three figures in the Con- 
stant are decimals, so when you divide 
the Turns per Inch by them always have 
three declrr.al places. 

The Turrs per Inch divided by Constant 
will give you Speed Gear. 

Suppose you want to put in 19.3 turns 
per inch, you must add 2 ciphers after the 
19.3, so as to have as many decimals as 
there are in the Constant. 

Example : 
.275)19.300(70 speed gear reciuired. 
19.25 



.50 
If you wish to add 1/16 of an inch for 
thickness of Spindle bands, place your 
terms as follows: 

40X48X18X97X 7 

• =Constant. 

40X35X19X12X13X22 

If a 7/8 whirl and 1 1/16 front roll, place 
as follows: 

40X48X18X 6X 8xl6X 7 

;=Constant. 

40X35X19X12X 7X17X22 

If a 3/4 whirl and 1 1/8 front roll, place 
as follows: 

40X48X18X 6X 4x 8X 7 

=Constant. 

40X35X19X12X 3X 9X22 
9:i 



All these examples will give Constant 
for Speed Gear. 



Note. — If you have not the Speed Gear 
required, you can overcome the difficulty 
by changing the 35 gear on the Com- 
pound. 



To Find Twist Gear. 

Suppose the length of stretch is 57; 
Inches, and a Roller Motion delivering 3 
Inches. This would equal 60 inch draw. 
You wish to put in 30 turns per inch, and 
you have an 18 inch Rim driving a 12 inch 
Cj^linder Pulley, and a 6 inch Cylinder 
driving a % whirl on spindle. 

Rule: — Multiply length of draw 60 
Inches, by Turns per inch 30, and by 
Cylinder Pulley 12 inches, and diameter 
of Whirl on Spindle % of an inch. Take 
this for your dividend. 

Then mviltiply the Rim 18 inches by 
Cylinder 6 inches. Take this for your 
divisor. 

Example: 

60X30X12X 3=64800 



18X 6X 4 = 432 
64800-^432=150. 
150^2=75 twist gear. 

Note. — Always divide your answer by 
2 on the D. & B. Mule, as it always works 
out twice the size of Twist Gear required. 

The reason you divide by 2 is: The 
Twist Gear revolves twice each draw, and 
on the Asa Lees's Mule the Twist Gear 
only revolves once each draw. 

94 



To Find Drag Gear. 

Suppose the Front Roll makes 19 revolu- 
tions per draw, and the Front Roll Spur 
Gear is 51, and Drag Gear Pinion is an 
18, and Back Shaft Gear 68, and revolu- 
tions of Back Shaft 3.5 for a 64 inch 
draw. 

Rule:— Multiply Rev. of Front Roll 19, 
by Front Roll Spur Gear 51, and by Drag 
Gear Pinion 18. Take these for your 
dividend. 

Then multiply Back Shaft Gear 68 by 
Rev. of Back Shaft 3.5. Take this for 
your divisor. 

Example: 

19X51X18=17442 



68X3.5 = 238 
17442-=-238=73 drag gear. 

Note. — For 60 inch draw use 3.28 in- 
stead of 3.5 for Rev. of Back Shaft and 
for 54 inch stretch use 2.95. 



To Find Draft. 

Suppose you have a 120 Crown Gear 
on, and 54 Back Roll Gear, and an 18 
Front Roll Gear, and 40 Change Gear. 
Find the Draft. 

Example: 

120X54=6480 



18X40= 720 
6480-=-720=9 of a draft. 



95 



TURNS OF SPINDLE TO ONE OF RIM 



Diam- 
eter 
of Rim 


10 incn Cylinder 


11 inch Cylinder 


Pulley 


Pulley 


Inches 


6 in.Cyl. 


6 in.Cyl. 


6 in.Cyl. 


6 in.Cyl 


^whirl 


1 iu.whirl! 

i 


X whirl 


1 in. whir 


12 


8.95 


1 
6.84 


1 8.14 


6.22 


13 


9.70 


7.41 


8.81 


6.73- 


14 


10.44 


7.99 


9.49 


7.26. 


15 


11.19 1 8.55 


10.17 


1 7.77 


16 


11.93 


9.12 


10.84 


8.29 


17 


12.68 


9.70 


11.52 


8.81 


18 


13.43 


10.27 


12.20 


9.33 


19 


14.19 


• 10.84 


12.90 


9.85 


20 


1 14.92 


11.41 


1 13.56 


10.37 




12 inch Cylinder 


13 inch Cylinder 




Pulley 


Pulley 


12 1 


7.46 


5.70 


6.88 


5.26 


13 


8.14 


6.17 


7.46 


5.70 


14 


8.70 


6.65 


8.02 


6.14 


15 


9.32 


7.12 


8.60 


6.57 


16 


1 9.94 J 


7.6-) 


9.17 


7.01 


17 


1 10.56 ^ 


8.08 


9.75 


7.46. 


18 1 


11.19 


8.56 


10.33 


7.90' 


19 1 


11.82 


9.03 


10.91 


8.32: 


20 1 


12.43 


9.50 i 


11.47 


8.77 



When finding turns of spindle to one o 
Rim, there is 1/16 of an inch added foi 
thickness of spindle band, to the Cylinde; 
and Whirl. 

The 6 inch Cylinder is reduced to six 
teenths. This is got by multiplying 1 
by 6, which equals 96, and 1/16 added fo 
thickness of band equals 97. 

96 



There are 12 sixteenths in 3/4 of an 
inch, and 1/16 added equals 13. 

There are 16 sixteentlis in 1 inch, and 
1/16 added equals 17. 

Suppose you have on an 18 inch Rim, 
ind a 12 inch Cylinder Pulley, a 6 inch 
Cylinder, and a % inch Whirl. 

Place them as follows: 
18x97=1746 1746^156=11.19 turns. 



12X13= 156 



Suppose the whirl was 1 inch instead 
of 3/4. Place as follows: 
18X97=1746 



12X17= 204 
1746^204=8.56 turns of spindle to one 
Df rim. 



NUMBERING YARNS. 

For every revolution of Reel handle, the 
Reel revolves twice ard winds on 1% 
vards at each revolution of Reel. If the 
landle has made 40 i evolutions, the Reel 
las made 80 revolutions, and SO times 
IV2 yards equals 120 yards or 1 Lea. 

Suppose 12 J yards of yarn weighs 25 
grains. You divide the 25 into 1000 and 
his gives the Number or Count of the 
Yarn. 

j Example: 1000-^25 grs.=40s. yarn. 

1 The reason for dividing 1000 by the 
;veight (in grains) of 120 yards is because 
1-20 yards is eoual to 1 '7 of 840 yards, or 
■:. hark, and 1000 equals 1/7 of 7000 grains, 
)r 1 lb. 

97 



RING SPINNING FRAME. 
To Find Draft. 

Suppose you have on an 84 Back Roll 
Gear, and a 40 Change Gear, a 120 Crown 
Gear, a 30 Front Roll Gear, and the Back 
Roll is % of an inch diameter, and the 
Front Roll 1 inch diameter or 8 eights. 

Rule: — Multiply Back Roll Gear 84, by 
Crown Gear 120, and by diameter of Front 
Roll 1 inch, or 8 eights. Take this for a; 
dividend. ; 

Then multiply Change Gear 40 by Front- 
Roll Gear 30 and diameter of Back Roll' 
7 eights. ". 

Example : 

84X120X8 

==9.6 draft. 

40X 30X7 



To Find Constant for Draft Gear. 

Rule: — Proceed exactly as when finding 
draft, but leave out the Draft Gear. 
Example.: 

84X120X8 

=384 constant. 

30X7 
Constant divided by draft required 
gives Draft Change Gear. 

Example: 384 (constant) -=-9.6 draft=40 
change gear. 

To Find "Turns per Inch" on the Whitin 
Spinning Frame. 

Rule:— Multiply Front Roll Gear 108, by 
Stud Gear 74, and by diameter of Cylin- 
der 7 inches. Take these for a dividend. 



Then multiply Twist Gear (which we 
will suppose to be) 40. by Cylinder Gear 
36. and diameter of whirl % inch and 
circumference of Front Roll 3.1416. 
Example: 
108X74X7 

^1^16.48 turns per inch. 

40X36X.75 X3.1416 
! Deduct 117c for slippage and thickness 
lof bands. 

16.48 less 119f=14.65. Actual turns per 
'inch. 



To Find Constant for Twist Gear on 
Whitin Frame. 

Rule: — Proceed as when finding "ti;rns 
per inch," but omit the Twist Gear. 
Example: 

108X74X7 

=659 

36X. 75X3. 1416 
Deduct ll^'f from 659=586 Constant. 
Constant divided by '"turns per inch" 
gives Twist Gear. 

Constant 586 divided by 14 turns per 
inch equals 42 Twist Gear. 



To Find Turns Per Inch on the H. and B. 
Frame. 

Rule:— Multiply Front Roll Gear 84, by 
Jack Gear 72, and diameter of Cvlinder 
7 inches. Take these for a dividend. 

Then multiply Twist Gear (suppo.sed to 
be) 40. by Cylinder Gear 21. and bv diam- 
eter of Whirl "s of an inch, and circum- 
ference of Front Roll 3.1416. 
99 



Example: 

84X72X7X8 

=1 8.33 

40X21X7X3.1416 
Deduct 15% from 18.33 on H. and B. 
Frames. 

18. 33X. 85=15. 58 actual turns per inch. 



Constant for Twist Gear on H. and B 
Frame. 

Rule: — Proceed as when finding turns 
per inch, but omit Twist Gear. 
Example: 

84X72X7X8 

=733 

21X7X3.1416 
Deduct 15% from 733. 
733 X. 85=623 Constant. 
Constant divided by turns per inch 
gives Twist Gear. 

(Constant) 623-:-15.58 (turns per inch)= 
40 T. G. 



A fixed rule cannot be given for the 
weights of travellers, as an inferior grade 
of cotton, a large draft, and a larger 
ring, requires a lighter traveller. Whilst 
good stock, and more twist in the yarn, 
also the spindles running quicker, re- 
quires a heavier traveller, although spin- 
ning the same Counts or Numbers. 



100 



To Find Average Counts Being Spun. 

Rule: — Proceed exactly as when finding 
average numbers given on the Mule. 

Keep the spindle rail and roller beam 
level, the spindle perfectly upright, or 
vertical and in the centre of the ring, 
when the rail is at the highest and lowest 
point of traverse. 

The guide wires should be set exactly 
over centre of the spindle (with spindle 
band on). 



HORSE POWER REQUIRED. 

Spin- 
I.H.P. dies. 

Hopper Bale Breaker 2 

Automatic Feeder li/^ 

Opener 2 

Picker (Single Beater) 4 

Picker (Double Beater) 8 

Flat Card 1 

Sliver Lap Machine V2 

Ribbon Lap Machine 1 

6 Head Single Nip Comber... % 

8 Head Single Nip Comber... 1 

Drawing Frame (12 Deliveries) IVz 

Slubbing Frame 1 45 

Intermediate Frame 1 65 

Roving Frame 1 85 

Jack Frame 1 105 

Fine Mule 1 130 

Coarse Mule 1 115 

Ring Spinning Frame 1 75 



WOONSOCKET MACHINE 
AND PRESS CO. 

=WOONSOCKET, R. I.^= 



Builders of 
Fly Frames, Cloth 
Presses,Cloth Trim= 
mers, Woolen Card 
Feeds, Transmission 
Machinery, and 
Yarn Gassing Aiach= 
ines. 



DRAPER COMPANY 

HOPEDALE, MASS. 



Makers of the celebrated 
NORTHROP LOOM 
And all kinds of Ring 
Spinning Spindles, Rings 
etc., Twisters, Spoolers, 
Banding Machines, 
Warpers, Balling Mach- 
ines, and Reels. 



SACO AND PETTEE 

Builders of 
Revolving Flat Card, 
Railway Heads, 
Drawing Frames, 
Roving Frames, 
Spinning Frames, 
Spoolers and Reels, 

MAIN OFFICE: 

NEWTON UPPER FALLS, MASS., U. S. A. 

WORKS : 
NEWTON UPPER FALLS, AND BIDDEFORD, ME. 

SOUTHERN AGENT: 
A. H. WASHBURN, CHARLOTTE, N. C. 



The Whitin Machine Works 

WHITINSVILLE, MASS., U. S. A 



Builders of Revolving Flat 
Cards, Spoolers, Sliver Lap 
Machines, Quillers, Ribbon 
Lap Machines, Reels, Comb- 
ing Machines (high speed). 
Twisting Frames, Railway 
Heads, Plain Looms, Drawing 
Frames, Drop Box Looms, 
Roving Machines, Dobbies, 
Spinning Frames, and all com- 
ponent parts. 



Southern Offices : 
Charlotte, N. C. and Atlanta, Ga. 

Stuart W. Cramer, Southern Agt. 



// you are contemplating 
building, or ctianging over 
your old macliinery, write to 
the . . . 

METALUC DRAWING 
ROLL COMPANY 



for prices and advantages of 
ttieir 



METALLIC ROLLS 

25 to 33 fo more production 
guaranteed, tlian can be re= 
ceived from any leattier roil, 

INDIAN ORCHARD, MASS. 



LIBRARY OF CONGRESS 

illlilliililllilllillliil 

018 533 836 8 • 



